Evaluate the power, and write the result in the form a + bi. (Simplify your answer completely.)

Question

i¹⁴⁰⁰

Answer 1

Using rules of exponents (a^(b*c) = (a^b)^c = (a^c)^b) we can rewrite this as i^(1400) = i^(350*4) = (i^4)^350. i^2 = -1 so i^4 = 1. Therefore, the original problem simplifies (i^4)^350 = (1)^350 = 1. So the final answer is 1. Using this same logic, we can see that i raised to a power which is a multiple of 4 will always equal 1.

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