Which of the following is equivalent to the complex number i^(21) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Determine pattern of powers: Determine the pattern of powers of i. The powers of i follow a cyclical pattern: i^1 = i i^2 = -1 i^3 = -i i^4 = 1 Then the pattern repeats every 4 powers.Reduce exponent modulo 4: Reduce the exponent 21 modulo 4 to find its equivalent in the pattern. 21 mod 4 = 1 This means that i^(21) is equivalent to i^(1) in the pattern.Match reduced exponent to pattern: Match the reduced exponent to the pattern. Since 21 mod 4 = 1, we look at the pattern and see that i^1 = i.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following is equivalent to the complex number
i^(21) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{21}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $i$ $\newline$ (C) $-1$ $\newline$ (D) $-i$

View step-by-step help

Full solution

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

i^{21}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Determine pattern of powers: Determine the pattern of powers of $i$ . $\newline$ The powers of $i$ follow a cyclical pattern: $\newline$ $i^1 = i$ $\newline$ $i^2 = -1$ $\newline$ $i^3 = -i$ $\newline$ $i^4 = 1$ $\newline$ Then the pattern repeats every $4$ powers.
Reduce exponent modulo $4$ : Reduce the exponent $21$ modulo $4$ to find its equivalent in the pattern. $\newline$ $21 \mod 4 = 1$ $\newline$ This means that $i^{21}$ is equivalent to $i^{1}$ in the pattern.
Match reduced exponent to pattern: Match the reduced exponent to the pattern. $\newline$ Since $21 \mod 4 = 1$ , we look at the pattern and see that $i^1 = i$ .