Which of the following is equivalent to the complex number i^(6) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Step 1: Define i as the imaginary unit: To solve for i^(6), we need to remember that i is the imaginary unit, which is defined by the property that i^2 = -1. We can use this property to simplify i^(6). i^(6) = (i^2)^(3)Step 2: Simplify i^(6) using the property of i^2: Now we apply the property that i^2 = -1. (i^2)^(3) = (-1)^(3)Step 3: Apply the property to calculate (-1)^(3): Next, we calculate the value of (-1)^(3). (-1)^(3) = -1Step 4: Determine the value of i^(6): Therefore, i^(6) is equivalent to -1.

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Which of the following is equivalent to the complex number
i^(6) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{6}$ ? $\newline$ 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

Full solution

Q. Which of the following is equivalent to the complex number

i^{6}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Step $1$ : Define $i$ as the imaginary unit: To solve for $i^{6}$ , we need to remember that $i$ is the imaginary unit, which is defined by the property that $i^2 = -1$ . We can use this property to simplify $i^{6}$ . $\newline$ $i^{6} = (i^2)^{3}$
Step $2$ : Simplify $i^{6}$ using the property of $i^2$ : Now we apply the property that $i^2 = -1$ . $\newline$ $(i^2)^{3} = (-1)^{3}$
Step $3$ : Apply the property to calculate $(-1)^3$ : Next, we calculate the value of $(-1)^3$ . $\newline$ $(-1)^3 = -1$
Step $4$ : Determine the value of $i^{6}$ : Therefore, $i^{6}$ is equivalent to $-1$ .