Which of the following is equivalent to the complex number i^(30) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Recognizing the Power Cycle: To solve for i^(30), we need to recognize that the powers of i repeat in a cycle of four: i, -1, -i, and 1. This is because i^2 = -1, i^3 = -i, and i^4 = 1. After every fourth power, the cycle repeats.Dividing the Exponent by 4: To find the equivalent of i^(30), we can divide the exponent by 4 and look at the remainder to determine where we are in the cycle. The division is 30 ÷ 4, which equals 7 with a remainder of 2.Determining the Equivalent of i^(30): Since the remainder is 2, we look at the second position in the cycle of i, which is -1. Therefore, i^(30) is equivalent to -1.

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Which of the following is equivalent to the complex number
i^(30) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{30}$ ? $\newline$ 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^{30}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Recognizing the Power Cycle: To solve for $i^{30}$ , we need to recognize that the powers of $i$ repeat in a cycle of four: $i$ , $-1$ , $-i$ , and $1$ . This is because $i^2 = -1$ , $i^3 = -i$ , and $i^4 = 1$ . After every fourth power, the cycle repeats.
Dividing the Exponent by $4$ : To find the equivalent of $i^{30}$ , we can divide the exponent by $4$ and look at the remainder to determine where we are in the cycle. The division is $30 \div 4$ , which equals $7$ with a remainder of $2$ .
Determining the Equivalent of $i^{30}$ : Since the remainder is $2$ , we look at the second position in the cycle of $i$ , which is $-1$ . Therefore, $i^{30}$ is equivalent to $-1$ .