Which of the following is equivalent to the complex number i^(9) ? Choose 1 answer: (A) 1 (B) i (c) -1 (D) -i

Complex number definition: To find the equivalent of the complex number i^(9), we need to remember that i is the imaginary unit, which is defined by i^2 = -1. We can simplify i^(9) by breaking it down into powers of i^2 and the remaining factor of i. i^(9) = (i^2)^(4) * iSimplifying i^(9): Now we simplify (i^2)^(4). Since i^2 = -1, we have: (i^2)^(4) = (-1)^(4)Calculating (-1)^(4): We calculate (-1)^(4). Any even power of -1 is 1, so: (-1)^(4) = 1Multiplying by i: Now we multiply the result by the remaining factor of i: 1 * i = iFinal result: Therefore, i^(9) is equivalent to i. The correct answer from the given choices is (B) i.

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Which of the following is equivalent to the complex number
i^(9) ?
Choose 1 answer:
(A) 1
(B)
i
(c) -1
(D)
-i

Which of the following is equivalent to the complex number $i^{9}$ ? $\newline$ 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^{9}

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

i

\newline

(C)

-1

\newline

(D)

-i

Complex number definition: To find the equivalent of the complex number $i^{9}$ , we need to remember that $i$ is the imaginary unit, which is defined by $i^2 = -1$ . We can simplify $i^{9}$ by breaking it down into powers of $i^2$ and the remaining factor of $i$ . $\newline$ $i^{9} = (i^2)^{4} \cdot i$
Simplifying $i^{9}$ : Now we simplify $(i^2)^{4}$ . Since $i^2 = -1$ , we have: $\newline$ $(i^2)^{4} = (-1)^{4}$
Calculating $(-1)^4$ : We calculate $(-1)^4$ . Any even power of $-1$ is $1$ , so: $\newline$ $(-1)^4 = 1$
Multiplying by i: Now we multiply the result by the remaining factor of i: $\newline$ $1 \times i = i$
Final result: Therefore, $i^{9}$ is equivalent to $i$ . The correct answer from the given choices is (B) $i$ .