Question

medctive deAL piy vand..Mama Africa Braccomputer appsScrible Toolbarkit2-4: MathXL: Complex Numbers & Add/SubtractionAssignment is past due (05/12.4.10Question HelpTamara says that raising the number i to any integer power results in either -1 or 1 as the result, since i ? = - 1. Do you agree with Tamara? ExplainSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. Tamara is correct. Checking a single value of a function is sufficient to determine trends for all input values.O B. Tamara is incorrect. For integer n," is only certain to be 1 or - 1 if n is even. If n is odd, " could be(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)OC. Tamara is correct. Starting with i 2 = -1, "can be found for any n by raising - 1 to the power of 2n, which is guaranteed to be - 1 or 1.OD. Tamara is incorrect. Any integer could be equal to i" if n can be any integer.Click to select and enter your answer(s) and then click Check Answer.All parts showingClear AllCheck AnswerReview progressQuestion 1of 10BackNext >

Answer 1

Given,

The power of i is any integer.

The power of i is even number than the value is -1 or 1.

As know that,

$\begin{gathered} \sqrt[]{-1}=i \\ -1=i^2 \\ i^3=i^2\times i \\ i^3=-1^{}\times\sqrt[]{-1} \\ i^4=i^2\times i^2 \\ i^4=-1\times-1=1 \end{gathered}$

So,

Tamara is incorrect. For integer n, i^n is certain to be 1 or -1 if n is even. if n is odd, i^n could be (sqrt(-1)) pr (-sqrt(-1)).

Hence, option b is correct.