Which of the following is equivalent to the complex number i^(17) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Introduction: To find the equivalent of i^(17), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can simplify i^(17) by breaking it down into powers of i^2.Breaking down i^(17): Since i^2 = -1, we can express i^(17) as (i^2)^(8) * i. This is because 17 = 2*8 + 1, and we are using the property that (i^2)^n = i^(2n).Simplifying (i^2)^(8) * i: Now we simplify (i^2)^(8) * i. Since i^2 = -1, we have (-1)^(8) * i. We know that any even power of -1 is 1, so (-1)^(8) = 1.Final result: Multiplying 1 by i gives us i. Therefore, i^(17) is equivalent to i.

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Which of the following is equivalent to the complex number
i^(17) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{17}$ ? $\newline$ 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^{17}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Introduction: To find the equivalent of $i^{17}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can simplify $i^{17}$ by breaking it down into powers of $i^2$ .
Breaking down $i^{17}$ : Since $i^2 = -1$ , we can express $i^{17}$ as $(i^2)^{8} \cdot i$ . This is because $17 = 2 \cdot 8 + 1$ , and we are using the property that $(i^2)^n = i^{2n}$ .
Simplifying $(i^2)^{8} \cdot i$ : Now we simplify $(i^2)^{8} \cdot i$ . Since $i^2 = -1$ , we have $(-1)^{8} \cdot i$ . We know that any even power of $-1$ is $1$ , so $(-1)^{8} = 1$ .
Final result: Multiplying $1$ by $i$ gives us $i$ . Therefore, $i^{17}$ is equivalent to $i$ .