Which of the following is equivalent to the complex number i^(20) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Definition of i: To solve for i^(20), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can use this property to simplify i^(20). i^(20) = (i^2)^(10) = (-1)^(10)Simplifying i^(20): Since (-1)^(10) is raising -1 to an even power, the result will be 1. (-1)^(10) = 1Result of i^(20): Now we have found that i^(20) is equivalent to 1, which matches one of the given choices.

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Which of the following is equivalent to the complex number
i^(20) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{20}$ ? $\newline$ 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^{20}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Definition of i: To solve for $i^{20}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can use this property to simplify $i^{20}$ . $\newline$ $i^{20} = (i^2)^{10} = (-1)^{10}$
Simplifying $i^{20}$ : Since $(-1)^{10}$ is raising $-1$ to an even power, the result will be $1$ . $\newline$ $(-1)^{10} = 1$
Result of $i^{20}$ : Now we have found that $i^{20}$ is equivalent to $1$ , which matches one of the given choices.