Which of the following is equivalent to the complex number i^(5) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Introduction: To find the equivalent of i^(5), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can simplify i^(5) by breaking it down into i^(4) * i^(1).Simplifying i^(5): We know that i^(4) is equal to (i^2) * (i^2). Since i^2 = -1, we can substitute to find that i^(4) = (-1) * (-1) = 1.Multiplying i^(4) and i^(1): Now that we have i^(4) = 1, we can multiply it by i^(1) to find i^(5). So, i^(5) = i^(4) * i^(1) = 1 * i = i.

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Which of the following is equivalent to the complex number
i^(5) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{5}$ ? $\newline$ 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^{5}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Introduction: To find the equivalent of $i^{5}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can simplify $i^{5}$ by breaking it down into $i^{4} \cdot i^{1}$ .
Simplifying $i^{5}$ : We know that $i^{4}$ is equal to $(i^{2}) \cdot (i^{2})$ . Since $i^{2} = -1$ , we can substitute to find that $i^{4} = (-1) \cdot (-1) = 1$ .
Multiplying $i^{4}$ and $i^{1}$ : Now that we have $i^{4} = 1$ , we can multiply it by $i^{1}$ to find $i^{5}$ . So, $i^{5} = i^{4} \cdot i^{1} = 1 \cdot i = i$ .