Which of the following is equivalent to the complex number i^(15) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Define i as Imaginary Unit: To solve for i^(15), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can simplify i^(15) by breaking it down into powers of i^2.Find Largest Multiple of 4: First, we find the largest multiple of 4 that is less than or equal to 15, because i^4 = (i^2)^2 = (-1)^2 = 1. The largest multiple of 4 less than or equal to 15 is 12.Express i^(15) as i^(3): We can express i^(15) as i^(12) * i^(3). Since i^(12) is a multiple of i^(4), it simplifies to 1. So, i^(15) simplifies to i^(3).Simplify i^(3): Now we need to simplify i^(3). We know that i^(2) = -1, so i^(3) = i^(2) * i = -1 * i = -i.Final Answer: Therefore, i^(15) is equivalent to -i, which corresponds to answer choice (D).

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Which of the following is equivalent to the complex number
i^(15) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{15}$ ? $\newline$ 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^{15}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Define $i$ as Imaginary Unit: To solve for $i^{15}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can simplify $i^{15}$ by breaking it down into powers of $i^2$ .
Find Largest Multiple of $4$ : First, we find the largest multiple of $4$ that is less than or equal to $15$ , because $i^4 = (i^2)^2 = (-1)^2 = 1$ . The largest multiple of $4$ less than or equal to $15$ is $12$ .
Express $i^{15}$ as $i^{3}$ : We can express $i^{15}$ as $i^{12} \times i^{3}$ . Since $i^{12}$ is a multiple of $i^{4}$ , it simplifies to $1$ . So, $i^{15}$ simplifies to $i^{3}$ .
Simplify $i^{3}$ : Now we need to simplify $i^{3}$ . We know that $i^{2} = -1$ , so $i^{3} = i^{2} \cdot i = -1 \cdot i = -i$ .
Final Answer: Therefore, $i^{15}$ is equivalent to $-i$ , which corresponds to answer choice $(D)$ .