1. The Product of powers property: 2. The Power of a power property: In this case, given: You need to follow these steps in order to simplify it: 1. Apply the Product of powers property: 2. Apply the Power of a power property: 3. Finally, since and , you get: Tasty Edits simplifies video creation for online influencers by providing specialized tools to make content stand out for their audience. * Required Field Your Name: * Your E-Mail:... Explain the steps involved in adding two rational expressions. First, find a common denominator. Find all the factors. Multiply the numerators and the denominators of both fractions. Then, simplify. Combine the numerators last. on Edge Learn with flashcards, games, and more — for free. The Steps to simplifying the 4 + x² - 2 [1 -2x³ + 2x² + 13x - 3 /( x - 3)] are: Step 1: Find the quotient. Step 2: Subtract the result from 1. Step 3: Multiply the result by –2. Step 4: Add the result to 4 + x². What is Algebra? A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.See list of participating sites @NCIPrevention @NCISymptomMgmt @NCICastle The National Cancer Institute NCI Division of Cancer Prevention DCP Home Contact DCP Policies Disclaimer P...Step by Step Solution. Reformatting the input : Changes made to your input should not affect the solution: (1): "g4" was replaced by "g^4". 1 more similar replacement (s). (2): Dot was discarded near "1.j". Step 1 : Trying to factor as a Difference of Squares : 1.1 Factoring: es-jpg4.The Steps to simplifying the 4 + x² - 2 [1 -2x³ + 2x² + 13x - 3 /( x - 3)] are: Step 1: Find the quotient. Step 2: Subtract the result from 1. Step 3: Multiply the result by –2. Step 4: Add the result to 4 + x². What is Algebra? A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.Water is sometimes removed from the products of a reaction by placing the products in a closed container with excess P4O10. Water is absorbed by the following reaction. P4O10 + 6H2O es001-1.jpg 4H3PO4 What is the mole ratio of water to H3PO4? Do not simplify the ratio. Hes001-2.jpgO:Hes001-3.jpgPOes001-4.jpg = :4 Algebra 2 Module 1 Review. How can the order of operations be used to simplify expressions? Click the card to flip 👆. By providing a set of rules on how to follow a foolproof order of operations when evaluating expressions, ensuring that everyone gets to the same answer once the expression is simplified. Click the card to flip 👆. Select all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the …Explanation: To solve the equation 1/3a2 - 1/a = 1/6a2, we need to multiply every term in the equation by the common denominator, which is 6a2. This gives us 2a - 6 = a. Now, we can combine like terms and simplify the equation by subtracting 'a' from both sides. This gives us a - 6 = 0. Finally, we can solve for 'a' by adding 6 to both sides ...Calculus. Simplify (e^x-1)/ (e^ (-x)-1) ex − 1 e−x − 1 e x - 1 e - x - 1. Nothing further can be done with this topic. Please check the expression entered or try another topic. ex −1 e−x − 1 e x - 1 e - x - 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step ...Algebra 2 Module 1 Review. How can the order of operations be used to simplify expressions? Click the card to flip 👆. By providing a set of rules on how to follow a foolproof order of operations when evaluating expressions, ensuring that everyone gets to the same answer once the expression is simplified. Click the card to flip 👆. 1 / 11.The formula es001-1.jpg gives the time it takes in seconds, T, for a pendulum to make one full swing back and forth, where L is the length of the pendulum, in feet. To the nearest foot, what is the length of a pendulum that makes one full swing in 1.9 s? Use 3.14 fores001-2.jpg .We use the power rule to simplify the above equation. For the same base, ... How much would an order of 1 slice of cheese pizza and 3 sodas cost? A. $3.25 B. $5.25 C ...Precalculus. Determine if Odd, Even, or Neither f (x)=x. Step 1. Find . Tap for more steps... Find by substituting for all occurrence of in . Remove parentheses. Step 2.Click here 👆 to get an answer to your question ️ A town predicts that its population will double in e^(ln 10)/2ln e years. Simplify the expression. In how mClick here 👆 to get an answer to your question ️ Exercise #5: Simplify each of the following powers of i. i^1=i i^2= i^3= i^4= i^5= i^6= i^7= i^8= We see, the. ... Study Resources / algebra / complex numbers. Question. Exercise #5: Simplify each of the following powers of i. i^1=i i^2= i^3= i^4= i^5= i^6= i^7= i^8= We see, then, from this pattern that every …The expression can be written as a single radical by covertong the expression to a rational format such that both the denominator and numerator have the same base as y¼. Numerator = The 4th root of y³ = y¾; Denominator = squareroot of y = y½; Using indices:. Division sign signifies the powers should be subtracted; Therefore, the expression can …Feb 23, 2020 · 7 6 5 00 8 2 1 3 4 3. 456 4. 4 and Decide whether each statement is TRUE or FALSE. If the statement is FALSE, correct the statement. 1. 2. 23 21 and 2 … 2 are vertical angles. 41 and 5 are corresponding angles. 2 and 5 are alternate exterior angles. 6 are alternate interior angles. 5. 5. Compare and contrast the absolute value of a real number to that of a complex number. imaginary number complex plane real number negative always positive. We have an …The es001-jpg is an advanced and versatile expression that is widely regarded as one of the most innovative in the industry. Developed by a team of experts, it combines cutting-edge technology, intuitive design, and exceptional performance to provide users with a seamless and immersive experience.Jan 26, 2018 · This relationship is established due to the fact that a full circle (or one revolution) encompasses 360° or 2π radians. Hence, to convert from radians to degrees, the formula is (number of radians) * (180/π). For instance, if you have 2 radians and you want to convert it to degrees, the calculation would be as follows: 2 * (180/π) = roughly ... Therefore, the like radical to 3√54 is 3√ (2 * 3²). 1. Start with the given radical: 3√54. 2. Break down 54 into prime factors: 54 = 2 * 3². 3. Rewrite the radical using the prime factorization: 3√ (2 * 3²). 4. The like radical is then 3√ (2 * 3²), as it represents the same value as the original radical, 3√54.The given expression can be evaluated by using following steps: Step 1 - Multiply numerator and denominator by . Step 2 - Multiply numerator and denominator by . Step 3 - Further simplify the above expression. Step 4 - Rearrange the above expression. The simplified form of is given by the expression: . For more information, …Step 1: Enter the formula for which you want to calculate the domain and range. The Domain and Range Calculator finds all possible x and y values for a given function. Step 2: Click the blue arrow to submit. Choose "Find the Domain and Range" from the topic selector and click to see the result in our Calculus Calculator ! Examples . Find the Domain and …In other words, it does not fall under the classification of being even or odd. Examples of How to Determine Algebraically if a Function is Even, Odd, or Neither. Example 1: Determine algebraically whether the given function is even, odd, or neither. [latex]f\left( x \right) = 2{x^2} – 3[/latex] I start with the given function [latex]f\left ...Step 1: Simplify the rational function. i.e., Factor the numerator and denominator of the rational function and cancel the common factors. Step 2: Set the denominator of the simplified rational function to zero and solve. Here is an example to find the vertical asymptotes of a rational function.Check all of the boxes that apply. B. 4,5. If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions. The value of c could be 5 or any number greater than 5. Identify the graph of the inequality 2 (2x - 1) + 7 < 13 or -2x + 5 -10. C.Create an account to view solutions. 1 / 4. Find step-by-step Precalculus solutions and your answer to the following textbook question: Simplify each power of i to i, 1,-i, or -1. $$ i^2 $$.Select all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the …Answer: Denominator of 1. Step-by-step explanation: An expression can be written in rational form by writing it as a fraction with a denominator of 1. HOPES THIS HELPS!We know that cube root can also be written as the power of 1/3, So. Multiplying the power with both variables. Simplifying the equation to get final form. As we can see that it is similar to the option B which is. B) x superscript five-thirds Baseline y superscript one- third. the correct option is BSelect all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the exponents within the parentheses instead of subtracting. The correct simplified form is x to the two-fifths power. <3 Learn with flashcards, games, and more — for free.5 PRACTICE PROBLEM. Simplify the following expression and write the answer in standard form: 5/ (3 + i) (1 - i) 6 PRACTICE PROBLEM. Evaluate the following expression for x = 2i: (x2 + 12)/ (3 - x) 3a + 2 − 6aa2 − 4 = 1a − 2. The students is incorrect. There are no solutions to this equation because first, you would find the LCD which is (a2) (a2). Next, you would simplify making 3 (a2)6aa2. Then, you would expand making 3a6a2. The next step is adding 6 to both sides. Soon, you get 4a/4 which equals 8/4. a circular oil spill continues to increase in size. the radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. the area of the circular region is given by the function a(r) = πr2, where r is the radius of the circle at time t. explain how to write a composite function to find the area of the region at time t.What is the simplest form of mc001-1.jpg D The gravitational force formula is mc001-1.jpg where F is the force between two objects, G is the constant of gravitation, m1 is the …X 2a-12 * X 2a+13 = X 4a+1. Now that the left side is simplified we can rewrite the equation. X 4a+1 = X 9a-7. Now that we have both sides simplified, we can see that we just need to make the exponents equal to each other. 4a+1 = 9a-7. Next, we need to algebraically solve for a. First add 7 to both sides. 4a+8 = 9a. Next, subtract 4a from both ...1) Rewrite the equation by factoring -8 from the radicand and taking the cube root to get -2 in front of the radical symbol. 2) The graph is reflected over the x-axis. 3) The graph is also reflected over the y-axis. 4) The graph is vertically stretched by a factor of 2. 5) The graph is translated ½ unit to the left.A town predicts that its population will double in es001-1. Jpg years. Simplify the expression. In how many years will the popul. ation of the town double?. SAT. Answer Comment. 1 answer: Alexxandr [17] 2 years ago. 8 0. Answer: 5. ... 5 · 1 answer. Tyler is preparing a speech on skateboarding for his physics class. For speech support, he is ...Create an account to view solutions. 1 / 4. Find step-by-step Precalculus solutions and your answer to the following textbook question: Simplify each power of i to i, 1,-i, or -1. $$ i^2 $$.Although even roots of negative numbers cannot be solved with just real numbers, odd roots are possible. For example:(-3) (-3) (-3)=cbrt (-27)Even though you are multiplying a negative number, it is possible to obtain a negative answer because you are multiplying it with itself an odd number of times. Let's walk through it a little more slowly ...Study with Quizlet and memorize flashcards containing terms like Which graph shows the solution to the equation 4x - 3 = 8?, To solve e4 - 3x = mr001-1.jpgx + 9 by graphing, …Simplify. Explain. heart outlined ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees. heart. 40. verified. Verified answer. Accenture has signed a multi year agreement to help a mobile telecom provider.A system with one solution has one meeting point for all the graphs. A system with infinite solutions is the same graph on top of itself. A system with no solution has graphs that don't all meet at one point (at least two are parallel).We will simplify, add, subtract, multiply, divide and use them in applications. Determine the Values for Which a Rational Expression is Undefined. If the denominator is zero, the rational expression is undefined. The numerator of a rational expression may be 0—but not the denominator. When we work with a numerical fraction, it is easy to avoid dividing …The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.. What is transformation? A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.. Given is a function, y = being transformed into y = . We see, that, in the function, …Video transcript. - So we have the graphs of two functions here. We have the graph y equals f of x and we have the graph y is equal to g of x. And what I wanna do in this …Mar 21, 2018 · Answer: years after the population will be doubled. Explanation: According to the question, There is a town which population is increasing per year. And, it will be doubled in years. Step by Step Solution. Reformatting the input : Changes made to your input should not affect the solution: (1): "s0" was replaced by "s^0". (2): Dot was discarded near "1.j". …Verified answer. Which statement is true about the primary intent to have work in process constraints?. 14. The value of a that makes the statement true is -5 . Given the following equation: [tex]3^ {-1 }\div 3^4 = 3^a [/tex] To determine the value of a that makes the ….Step by Step Solution. Reformatting the input : Changes made to your input should not affect the solution: (1): "s0" was replaced by "s^0". (2): Dot was discarded near "1.j". …Study with Quizlet and memorize flashcards containing terms like Use the formula for radian measure to calculate the measure of a central angle in a circle having a radius of 12 cm and intercepting an arc of 21 cm. es001-1.jpg The angle has a measure of _____ radians., Convert 1 radian to degrees. Round your answer to the nearest degree., …Step by Step Solution. Reformatting the input : Changes made to your input should not affect the solution: (1): "g4" was replaced by "g^4". 1 more similar replacement (s). (2): …Oct 26, 2019 · Es001-1.jpg - 13235712. denishastockdale21 denishastockdale21 26.10.2019 ... Substitute r(x) = 2√x and s(x)= √x and simplify (rs)(x) =2√x . √x (rs)(x) =2x ... Explain the steps involved in adding two rational expressions. First, find a common denominator. Find all the factors. Multiply the numerators and the denominators of both fractions. Then, simplify. Combine the numerators last. on Edge Learn with flashcards, games, and more — for free. For a computer to open any file, it needs to have a program associating it with that type of file, so if a computer does not open a JPG file, the computer needs an associated progr...Find more answers. plus. Ask your question. What is the measure of angle 2? es001-1.jpg = - 23560972. To simplify the given expression \((e^\frac{l^n}{2\ln e})\), we can use the property of logarithms that states \(\ln e = 1\). Therefore, the expression simplifies to \(e^\frac{l^n}{2}\). To find out in how many years the population of the town will double, we need to solve the equation where the initial population is multiplied by 2, which ... Cancelling 3n - 2 from Numerator & Denominator. = 4 (3n + 2) = 12n + 8. (8/ (6n - 4) ) * (9n² - 4²) = 12n +8. Learn more: find the product of the following 5pq,-7q - … What is the simplest form of mc001-1.jpg. (A) sqrt 2. Which expression should you multiply the numerator and denominator of mc001-1.jpg by to rationalize the denominator? C. What is mc002-1.jpg in simplest form? A. What is the simplest form of mc001-1.jpg. D. The gravitational force formula is mc001-1.jpg where F is the force between two ... Final answer: The composition of two functions (f ∘ g)(x) means to substitute g(x) into f(x).With the information given in the question, none of the options - A. f(x) + g(x), B. f(x) * g(x), C. g(x) - f(x), D. f(x) / g(x) - is the correct composite of f and g.Before we can do that, we need some vocabulary. The reciprocal of a fraction is found by inverting the fraction, placing the numerator in the denominator and the denominator in the numerator. The reciprocal of 23 2 3 is 32. 3 2. Since 4 is written in fraction form as 41, 4 1, the reciprocal of 4 is 14. 1 4.The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.. What is transformation? A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.. Given is a function, y = being transformed into y = . We see, that, in the function, …Step 1: Calculate the moles of sodium carbonate (Na2CO3) Number of moles = mass / molar mass Number of moles = 7.5 g / 105.99 g/mol (molar mass of Na2CO3) Number of moles = 0.0707 mol. Step 2: Determine the stoichiometry of the reaction From the balanced equation: 1 mol Na2CO3 reacts with 2 mol HCl to form 2 mol …Simplify. Explain. heart outlined ... (OH)3) are consumed in this reaction? 14KMnO4 + 4C3H5(OH)3 es001-1.jpg 7K2CO3 + 7Mn2O3 + 5CO2 + 16H2O. star. 5/5. heart. 24. How many moles of KMnO4 are consumed to form 0.886 moles of carbon dioxide? heart. 1. verified. Verified answer. A drink that contains 4 1/2 ounces of a proof …What is the pH of a solution in which the hydrogen ion concentration is 5.1 x 10-5 M? Group of answer choices 5.10 4.29 7.28 8.90 Hypothetical metal M has a molecular weight 174 g/mol and crystallizes in a body-centered cubic array of atoms in which the length of the unit cell'sStudy with Quizlet and memorize flashcards containing terms like Which graph shows the solution to the equation 4x - 3 = 8?, To solve e4 - 3x = mr001-1.jpgx + 9 by graphing, …Right triangle mc001-1.jpg has mc001-2.jpg, a = 6, and b = mc001-3.jpg. Use this information to find mc001-4.jpg. This question hasn't been solved yet! Not what you’re looking for? Submit your question to a subject-matter expert. Send to expert Send to expert Send to expert done loading.This relationship is established due to the fact that a full circle (or one revolution) encompasses 360° or 2π radians. Hence, to convert from radians to degrees, the formula is (number of radians) * (180/π). For instance, if you have 2 radians and you want to convert it to degrees, the calculation would be as follows: 2 * (180/π) = roughly ...adioabiola. The simplification of i²² is equal to; -1. According to the question; We are required to determine the value of i²². By complex numbers; i = √-1. i² = -1. i³ = -1 × √-1 = -1 × i = -i. i⁴ = i² × i² = -1 × -1 = 1.Simplify \(1 + 8 • 9\). If you missed this problem, review Example 2.1.8. Evaluate Algebraic Expressions. In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations. To evaluate an algebraic expression means to find the value of the expression when the …adioabiola. The simplification of i²² is equal to; -1. According to the question; We are required to determine the value of i²². By complex numbers; i = √-1. i² = -1. i³ = -1 × √-1 = -1 × i = -i. i⁴ = i² × i² = -1 × -1 = 1.The LCD is (m − 4) (m − 1). (m − 4) (m − 1). Clear the fractions by multiplying both sides of the equation by the LCD. Distribute. Remove common factors. Simplify. Solve the resulting equation. Check. The only algebraic solution was 4, but we said that 4 would make a denominator equal to zero. The algebraic solution is an extraneous ... 1) Rewrite the equation by factoring -8 from the radicand and taking the cube root to get -2 in front of the radical symbol. 2) The graph is reflected over the x-axis. 3) The graph is also reflected over the y-axis. 4) The graph is vertically stretched by a factor of 2. 5) The graph is translated ½ unit to the left. In today’s digital age, the need to convert multiple JPG files into a single PDF document is becoming increasingly common. One of the easiest and most convenient ways to convert mu...Simplify \(1 + 8 • 9\). If you missed this problem, review Example 2.1.8. Evaluate Algebraic Expressions. In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations. To evaluate an algebraic expression means to find the value of the expression when the …Study with Quizlet and memorize flashcards containing terms like Reactant A can participate in both of these reactions: 1) A + B es002-1.jpg C + D es002-2.jpgGrxn = -15.6 kJ 2) A + E es002-3.jpg F + G es002-4.jpgGrxn = -20.5 kJ Reaction 1 has a much higher rate than Reaction 2 under the same reaction conditions. Explain this observation in … 3a + 2 − 6aa2 − 4 = 1a − 2. The students is incorrect. There are no solutions to this equation because first, you would find the LCD which is (a2) (a2). Next, you would simplify making 3 (a2)6aa2. Then, you would expand making 3a6a2. The next step is adding 6 to both sides. Soon, you get 4a/4 which equals 8/4. Study with Quizlet and memorize flashcards containing terms like A car battery produces electrical energy with the following chemical reaction. Pb + PbO2 + 2H2SO4 es001-1.jpg; 2PbSO4 + 2H2O What is the mole ratio of PbO2 to water? How many moles of water are produced if 5.43 mol PbO2 are consumed?, The fuel used to power the booster rockets …Therefore, the like radical to 3√54 is 3√ (2 * 3²). 1. Start with the given radical: 3√54. 2. Break down 54 into prime factors: 54 = 2 * 3². 3. Rewrite the radical using the prime factorization: 3√ (2 * 3²). 4. The like radical is then 3√ (2 * 3²), as it represents the same value as the original radical, 3√54.Furthermore, expressions are a mathematical relationship that doesn't have an equality symbol. Examples of Expressions. 3x². 4x + y. 5x/y. x-3y². The word equivalent implies equal, so the expressions are equivalent, which means that they are equal. Given the expressions 2 (x - 5) + 1 and 2x - 9 These two expressions are equivalent or equal. Explain the steps involved in adding two rational expressions. First, find a common denominator. Find all the factors. Multiply the numerators and the denominators of both fractions. Then, simplify. Combine the numerators last. on Edge Learn with flashcards, games, and more — for free. Step 1 : Trying to factor as a Difference of Cubes: 1.1 Factoring: es3-jpg Theory : A difference of two perfect cubes, a3-b3 can be factored into (a-b) • (a2+ab +b2) Proof : (a …Select all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the …Click here 👆 to get an answer to your question ️ [SOLVED] Find the simplified product where mc001-1. jpg: mc001-2. jpg mc001-3. jpg mc001-4. jpg mc0…1. The Product of powers property: 2. The Power of a power property: In this case, given: You need to follow these steps in order to simplify it: 1. Apply the Product of powers property: 2. Apply the Power of a power property: 3. Finally, since and , you get:
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AirMeet is a platform which allows users to host virtual conferences, work meetings, and chats. It promises to do this without a lot of complicated setup. AirMeet, the online event...Using Properties to Simplify Expressions assignment 100% you will get a 100%. ... He realized that he lost es001-1.jpg of a dollar each hour that the store was closed ...Engineering. Computer Science. Computer Science questions and answers. Simplify each of the following powers of i. es^ (001)-1.jpg.Which numbers are solutions to the inequality 2x - 1 > x + 2? Check all of the boxes that apply. B 4,5. If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions. The value of c could be 5 or any number greater than 5. Identify the graph of the inequality 2(2x - 1) + 7 < 13 or -2x + 5 …Question: Simplify each of the following powers of i. es^(001)-1.jpg. Simplify each of the following powers of i. es^(001)-1.jpg. This question hasn't been solved yet!(1): "s0" was replaced by "s^0". (2): Dot was discarded near "1.j". Step 1 : Final result : es - jpg5 PRACTICE PROBLEM. Simplify the following expression and write the answer in standard form: 5/ (3 + i) (1 - i) 6 PRACTICE PROBLEM. Evaluate the following expression for x = 2i: (x2 + 12)/ (3 - x) Simplifying Powers of i. Step 1: Rewrite the power of i using the power of a power, and the product properties of exponents to write the expression using terms of i 2 = − 1, and i 4 = ( i 2) 2 ... One to any power is one. Multiply i i by 1 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Mechanical engineering college · Master's degree. Answer: Hence answer is i . Explanation: Given. i^ {37} i37 To find - solve Solurion: i^ {37} i37 (i^ {4})^ {9}\times i (i4)9×i (1)^ {9}\times \dot {1} (1)9×1˙ 1\times i 1×i {j} j. Click to rate: 4.7. (127 votes) Click here 👆 to get an answer to your question ️ Use the example as a model.Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees. heart. 40. verified. Verified answer. Accenture has signed a multi year agreement to help a mobile telecom provider. star. 4/5. heart. 4. verified. Verified answer. Which …Study with Quizlet and memorize flashcards containing terms like Which graph shows the solution to the equation 4x - 3 = 8?, To solve e4 - 3x = mr001-1.jpgx + 9 by graphing, …To convert a file from the JPG format to the DST format, download a program or application that performs the conversion. Then, open the JPG file inside the software and save it in ...Oct 19, 2021 · To simplify the given expressions, recall that (i) is the imaginary unit, defined as. (a) Therefore, (b) Therefore, In both cases, the expressions simplify to either t or -1 based on the properties of the imaginary unit (i) . The powers of t are reduced by exploiting the fact that , allowing for simplification and concise expression of the results. In the context of complex numbers, the imaginary unit ' i ' has a cyclic pattern of powers. Specifically, i^1 is i, i^2 is -1, i^3 is -i, and i^4 is 1. After this, the cycle repeats. ….