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Which of the following is equivalent to the complex number
i^(26) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{26}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $i$ $\newline$ (C) $-1$ $\newline$ (D) $-i$

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Compare linear, exponential, and quadratic growth

Full solution

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

i^{26}

?

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Recognize the pattern: Recognize the pattern of powers of $i$ . The powers of $i$ repeat in a cycle of $4$ : $i^1 = i$ , $i^2 = -1$ , $i^3 = -i$ , $i^4 = 1$ , and then the pattern repeats.
Determine the remainder: Determine the remainder when $26$ is divided by $4$ to find where in the cycle $i^{26}$ falls. $\newline$ $26$ divided by $4$ is $6$ with a remainder of $2$ .
Use the remainder: Use the remainder to determine the equivalent power of $i$ . $\newline$ Since the remainder is $2$ , $i^{26}$ is equivalent to $i^2$ .
Calculate $i^2$ : Calculate $i^2$ . $\newline$ We know from the pattern that $i^2 = -1$ .

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