What is the value of i raised to the power of 402?

B. -1 — The powers of i repeat in a cycle of four: i, -1, -i, 1. Dividing 402 by 4 gives a remainder of 2, so i raised to the power of 402 is equivalent to i squared, which is -1.

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$What is the value of i^{402} ?$

A. $1$
B. $- 1$
C. $i$
D. $- i$

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Correct answer: B — $- 1$

Solution

The powers of i repeat in a cycle of four: i, - 1, - i, 1 . Dividing 402 by 4 gives a remainder of 2, so i^{402} = i^{2} = - 1 .

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What is the value of i402?

Solution

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$What is the value of i^{402} ?$