Which of the following is equivalent to the complex number i^(34) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Define imaginary unit: To find the value of i^(34), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. The powers of i repeat in a cycle: i, -1, -i, 1, and then back to i.Find remainder of 34: We can find the remainder when 34 is divided by 4 because the powers of i repeat every 4th power. This will tell us which part of the cycle i^(34) falls on. 34 ÷ 4 = 8 remainder 2Determine i^(34) value: Since there is a remainder of 2, i^(34) corresponds to the second number in the cycle of i, which is -1.Final result: Therefore, i^(34) is equivalent to -1.

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Which of the following is equivalent to the complex number
i^(34) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{34}$ ? $\newline$ 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^{34}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Define imaginary unit: To find the value of $i^{34}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . The powers of $i$ repeat in a cycle: $i$ , $-1$ , $-i$ , $1$ , and then back to $i$ .
Find remainder of $34$ : We can find the remainder when $34$ is divided by $4$ because the powers of $i$ repeat every $4$ th power. This will tell us which part of the cycle $i^{34}$ falls on. $\newline$ $34 \div 4 = 8$ remainder $2$
Determine $i^{34}$ value: Since there is a remainder of $2$ , $i^{34}$ corresponds to the second number in the cycle of $i$ , which is $-1$ .
Final result: Therefore, $i^{34}$ is equivalent to $-1$ .