Which of the following is equivalent to the complex number i^(13) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Definition of i: To solve for i^(13), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can use the powers of i to simplify i^(13).Cycle of powers of i: The powers of i repeat in a cycle: i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. Then the cycle repeats: i^5 = i, i^6 = -1, and so on.Finding i^(13): To find i^(13), we can divide 13 by 4 to find how many full cycles of 4 there are and what the remainder is. The remainder will tell us the equivalent power of i that we need to find. 13 ÷ 4 = 3 with a remainder of 1.Equivalent of i^(13): Since the remainder is 1, i^(13) is equivalent to i^(1), which is simply i.Conclusion: Therefore, the equivalent of the complex number i^(13) is i, which corresponds to choice (B).

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Which of the following is equivalent to the complex number
i^(13) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{13}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $i$ $\newline$ (C) $-1$ $\newline$ (D) $-i$

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Math Problems

Algebra 1

Domain and range of quadratic functions: equations

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Q. Which of the following is equivalent to the complex number

i^{13}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Definition of i: To solve for $i^{13}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can use the powers of $i$ to simplify $i^{13}$ .
Cycle of powers of i: The powers of i repeat in a cycle: i^$1$ = i, i^$2$ = $-1$ , i^$3$ = -i, and i^$4$ = $1$ . Then the cycle repeats: i^$5$ = i, i^$6$ = $-1$ , and so on.
Finding $i^{13}$ : To find $i^{13}$ , we can divide $13$ by $4$ to find how many full cycles of $4$ there are and what the remainder is. The remainder will tell us the equivalent power of $i$ that we need to find. $\newline$ $13 \div 4 = 3$ with a remainder of $1$ .
Equivalent of $i^{13}$ : Since the remainder is $1$ , $i^{13}$ is equivalent to $i^{1}$ , which is simply $i$ .
Conclusion: Therefore, the equivalent of the complex number $i^{13}$ is $i$ , which corresponds to choice (B).