Which of the following is equivalent to the complex number i^(24) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Definition of i: To solve for i^(24), 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^(24).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. So, i^(24) can be simplified by dividing the exponent by 4 and looking at the remainder.Simplifying i^(24): Divide 24 by 4. The remainder of this division is 0, since 24 is a multiple of 4. This means that i^(24) is equivalent to i^(4 * 6), which is (i^4)^6.Dividing the exponent: Since i^4 = 1, then (i^4)^6 = 1^6. Any non-zero number to the power of 6 is just the number itself, so 1^6 = 1.Simplifying (i^4)^6: Therefore, i^(24) is equivalent to 1. The correct answer is (A) 1.

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Which of the following is equivalent to the complex number
i^(24) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{24}$ ? $\newline$ 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

Full solution

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

i^{24}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Definition of i: To solve for $i^{24}$ , 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 $i^{24}$ .
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. So, $i^{24}$ can be simplified by dividing the exponent by $4$ and looking at the remainder.
Simplifying $i^{24}$ : Divide $24$ by $4$ . The remainder of this division is $0$ , since $24$ is a multiple of $4$ . This means that $i^{24}$ is equivalent to $i^{4 \times 6}$ , which is $(i^4)^6$ .
Dividing the exponent: Since $i^4 = 1$ , then $(i^4)^6 = 1^6$ . Any non-zero number to the power of $6$ is just the number itself, so $1^6 = 1$ .
Simplifying $i^4$ ^ $6$ : Therefore, $i^{24}$ is equivalent to $1$ . The correct answer is (A) $1$ .