Which of the following is equivalent to the complex number i^(36) ? Choose 1 answer: (A) 1 (B) i (c) -1 (D) -i

Definition of i: To solve for i^(36), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can use the powers of i to simplify i^(36).Cycle of powers of i: The powers of i repeat in a cycle: i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. Then the cycle repeats itself. So, i^(36) can be simplified by dividing 36 by 4 and looking at the remainder.Simplifying i^(36): Divide 36 by 4. The quotient is 9 and the remainder is 0. This means that i^(36) is the same as (i^4)^9.Using the power of i: Since i^4 = 1, then (i^4)^9 = 1^9.Simplifying to 1: 1 raised to any power is still 1, so 1^9 = 1.Final result: Therefore, i^(36) is equivalent to 1.

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Which of the following is equivalent to the complex number
i^(36) ?
Choose 1 answer:
(A) 1
(B)
i
(c) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{36}$ ? $\newline$ 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^{36}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Definition of i: To solve for $i^{36}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can use the powers of $i$ to simplify $i^{36}$ .
Cycle of powers of i: The powers of i repeat in a cycle: i^$1$ = i, i^$2$ = $-1$ , i^$3$ = -i, and i^$4$ = $1$ . Then the cycle repeats itself. So, i^$36$ can be simplified by dividing $36$ by $4$ and looking at the remainder.
Simplifying $i^{36}$ : Divide $36$ by $4$ . The quotient is $9$ and the remainder is $0$ . This means that $i^{36}$ is the same as $(i^4)^9$ .
Using the power of $i$ : Since $i^4 = 1$ , then $(i^4)^9 = 1^9$ .
Simplifying to $1$ : $1$ raised to any power is still $1$ , so $1^9 = 1$ .
Final result: Therefore, $i^{36}$ is equivalent to $1$ .