Which of the following is equivalent to the complex number i^(16) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Understanding powers of i: To solve for i^(16), we need to remember the powers of i. The powers of i cycle in a pattern: i, -1, -i, 1, and then repeat. This is because i^2 = -1, i^3 = i^2 * i = -i, and i^4 = (i^2)^2 = 1.Finding the position of i^(16): Since the powers of i repeat every 4th power, we can divide the exponent by 4 to find where i^(16) lands in the cycle. 16 divided by 4 is 4, which means i^(16) is (i^4)^4.Simplifying (i^4)^4: We know that i^4 = 1. Therefore, (i^4)^4 = 1^4.Calculating 1^4: Calculating 1^4, we get 1, because any non-zero number to the power of 4 is itself.Final result: i^(16) = 1: So, i^(16) is equivalent to 1.

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Which of the following is equivalent to the complex number
i^(16) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{16}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $i$ $\newline$ (C) $-1$ $\newline$ (D) $-i$

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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^{16}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Understanding powers of i: To solve for $i^{16}$ , we need to remember the powers of $i$ . The powers of $i$ cycle in a pattern: $i$ , $-1$ , $-i$ , $1$ , and then repeat. This is because $i^2 = -1$ , $i^3 = i^2 \cdot i = -i$ , and $i^4 = (i^2)^2 = 1$ .
Finding the position of $i^{16}$ : Since the powers of $i$ repeat every $4$ th power, we can divide the exponent by $4$ to find where $i^{16}$ lands in the cycle. $\newline$ $16$ divided by $4$ is $4$ , which means $i^{16}$ is $(i^4)^4$ .
Simplifying $(i^4)^4$ : We know that $i^4 = 1$ . Therefore, $(i^4)^4 = 1^4$ .
Calculating $1^4$ : Calculating $1^4$ , we get $1$ , because any non-zero number to the power of $4$ is itself.
Final result: $i^{16} = 1$ : So, $i^{16}$ is equivalent to $1$ .