Which of the following is equivalent to the complex number i^(11) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Introduction: To solve for i^(11), 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^(11). i^(11) = i^(10) * i Since i^2 = -1, we can rewrite i^(10) as (i^2)^5. i^(11) = (i^2)^5 * i Now we simplify (i^2)^5. (i^2)^5 = (-1)^5 Since -1 raised to an odd power is -1, we have: i^(11) = -1 * i i^(11) = -i

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Which of the following is equivalent to the complex number
i^(11) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{11}$ ? $\newline$ 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^{11}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Introduction: To solve for $i^{11}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can use this property to simplify $i^{11}$ . $\newline$ $i^{11} = i^{10} \cdot i$ $\newline$ Since $i^2 = -1$ , we can rewrite $i^{10}$ as $(i^2)^5$ . $\newline$ $i^{11} = (i^2)^5 \cdot i$ $\newline$ Now we simplify $(i^2)^5$ . $\newline$ $(i^2)^5 = (-1)^5$ $\newline$ Since $-1$ raised to an odd power is $-1$ , we have: $\newline$ $i^{11} = -1 \cdot i$ $\newline$ $i^{11} = -i$