Math

Powers of i Calculator

Find iⁿ, which cycles through i, −1, −i and 1.

Calculated Output

Real part 0

Imaginary part (i) -1

Formula: iⁿ depends on n mod 4

Step-by-Step Breakdown

1. Values used:

2. Exponent n = 27

4. Real part = 0

5. Imaginary part = -1i

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The math behind it

i⁰ = 1, i¹ = i, i² = −1, i³ = −i, then it repeats. So iⁿ depends only on n mod 4.

i²⁷: 27 mod 4 = 3, so i²⁷ = −i.

What is i⁰?

i⁰ = 1, like any non-zero number raised to the zero power.