Which of the following is equivalent to the complex number i^(80) ? Choose 1 answer: (A) 1 (B) i (c) -1 (D) -i

Recognizing the pattern of powers: To solve for i^(80), 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. This pattern repeats every 4 powers of i.Dividing the exponent by 4: Since the pattern repeats every 4 powers, we can divide the exponent by 4 to find where i^(80) lands in the cycle. We calculate 80 ÷ 4 = 20, which means i^(80) is at the same position in the cycle as i^(4*20).Simplifying i^(4*20): i^(4*20) is equivalent to (i^4)^20. Since i^4 = 1, this simplifies to 1^20.Applying the rule of 1 raised to any power: 1 raised to any power is still 1, so 1^20 = 1. Therefore, i^(80) is equivalent to 1.

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Which of the following is equivalent to the complex number
i^(80) ?
Choose 1 answer:
(A) 1
(B)
i
(c) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{80}$ ? $\newline$ 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^{80}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Recognizing the pattern of powers: To solve for $i^{80}$ , 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. This pattern repeats every $4$ powers of $i$ .
Dividing the exponent by $4$ : Since the pattern repeats every $4$ powers, we can divide the exponent by $4$ to find where $i^{80}$ lands in the cycle. We calculate $80 \div 4 = 20$ , which means $i^{80}$ is at the same position in the cycle as $i^{4 \times 20}$ .
Simplifying $i^{4\times 20}$ : $i^{4\times 20}$ is equivalent to $(i^4)^{20}$ . Since $i^4 = 1$ , this simplifies to $1^{20}$ .
Applying the rule of $1$ raised to any power: $1$ raised to any power is still $1$ , so $1^{20} = 1$ . Therefore, $i^{80}$ is equivalent to $1$ .