Which of the following is equivalent to the complex number i^(28) ? Choose 1 answer: (A) 1 (B) i (C) -1 (D) -i

Definition of i: To solve for i^(28), 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^(28) by recognizing the pattern that occurs every four powers of i: i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. This pattern repeats every four powers.Pattern of powers of i: Since the powers of i repeat every four powers, we can divide the exponent 28 by 4 to find out how many full cycles of this pattern occur within i^(28). We perform the division: 28 ÷ 4 = 7. This means that i^(28) is equivalent to (i^4)^7.Dividing the exponent: Knowing that i^4 = 1, we can now simplify (i^4)^7 to 1^7. Since any non-zero number raised to any power is itself, 1^7 is simply 1.Simplifying (i^4)^7: Therefore, i^(28) is equivalent to 1, which corresponds to choice (A) in the given options.

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Which of the following is equivalent to the complex number
i^(28) ?
Choose 1 answer:
(A) 1
(B)
i
(C) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{28}$ ? $\newline$ 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^{28}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Definition of i: To solve for $i^{28}$ , 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 $i^{28}$ by recognizing the pattern that occurs every four powers of $i$ : $i^1 = i$ , $i^2 = -1$ , $i^3 = -i$ , and $i^4 = 1$ . This pattern repeats every four powers.
Pattern of powers of i: Since the powers of i repeat every four powers, we can divide the exponent $28$ by $4$ to find out how many full cycles of this pattern occur within $i^{28}$ . We perform the division: $28 \div 4 = 7$ . This means that $i^{28}$ is equivalent to $(i^4)^7$ .
Dividing the exponent: Knowing that $i^4 = 1$ , we can now simplify $(i^4)^7$ to $1^7$ . Since any non-zero number raised to any power is itself, $1^7$ is simply $1$ .
Simplifying $i^4$ ^ $7$ : Therefore, $i^{28}$ is equivalent to $1$ , which corresponds to choice $A$ in the given options.