Which of the following is equivalent to the complex number i^(31) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Recognizing the pattern of powers: To solve for i^(31), we need to recognize the pattern of powers of i. The powers of i cycle in a pattern: i, -1, -i, 1, and then repeat. Let's find the remainder when 31 is divided by 4 to determine where in the cycle i^(31) falls. 31 ÷ 4 = 7 remainder 3Determining the position in the cycle: Since the remainder is 3, i^(31) corresponds to the third number in the cycle of i, which is -i. This is because the cycle starts with i^1, and every fourth power returns to the beginning of the cycle.Finding the equivalent value: Therefore, i^(31) is equivalent to -i, which corresponds to choice (D).

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Which of the following is equivalent to the complex number
i^(31) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{31}$ ? $\newline$ 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^{31}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Recognizing the pattern of powers: To solve for $i^{31}$ , we need to recognize the pattern of powers of $i$ . The powers of $i$ cycle in a pattern: $i$ , $-1$ , $-i$ , $1$ , and then repeat. Let's find the remainder when $31$ is divided by $4$ to determine where in the cycle $i^{31}$ falls. $\newline$ $i$ $0$ remainder $i$ $1$
Determining the position in the cycle: Since the remainder is $3$ , $i^{31}$ corresponds to the third number in the cycle of $i$ , which is $-i$ . This is because the cycle starts with $i^1$ , and every fourth power returns to the beginning of the cycle.
Finding the equivalent value: Therefore, $i^{31}$ is equivalent to $-i$ , which corresponds to choice (D).