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Which of the following is equivalent to the complex number
i^(31) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{31}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $i$ $\newline$ (C) $-1$ $\newline$ (D) $-i$

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Domain and range of quadratic functions: equations

Full solution

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

i^{31}

?

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Recognizing the pattern of powers: To solve for $i^{31}$ , we need to recognize the pattern of powers of $i$ . The powers of $i$ cycle in a pattern: $i$ , $-1$ , $-i$ , $1$ , and then repeat. Let's find the remainder when $31$ is divided by $4$ to determine where in the cycle $i^{31}$ falls. $\newline$ $i$ $0$ remainder $i$ $1$
Determining the position in the cycle: Since the remainder is $3$ , $i^{31}$ corresponds to the third number in the cycle of $i$ , which is $-i$ . This is because the cycle starts with $i^1$ , and every fourth power returns to the beginning of the cycle.
Finding the equivalent value: Therefore, $i^{31}$ is equivalent to $-i$ , which corresponds to choice (D).

More problems from Domain and range of quadratic functions: equations

Question

h

is defined over the real numbers. This table gives a few values of

h

\newline

\begin{tabular}{lllll}

\newline

x

-6

1

-6

01

-6

001

-5

9

\newline

h(x)

-0

25

-0

74

-0

98

-1

0

\newline

\newline

What is a reasonable estimate for

\lim _{x \rightarrow-6} h(x)

\newline

1

\newline

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-2

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-1

\newline

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