Powers Of I Calculator

Calculate any power of the imaginary unit i using the four-step repeating cycle.

Last updated: March 2026 | By ForgeCalc Engineering

Powers Of I Solver

Imaginary unit

Exponent

Calculation Steps

1.Exponent: 5

2.Compute n mod 4 = 1

3.i^0 = 1

4.i^1 = i

5.i^2 = -1

6.i^3 = -i

7.Result: i^5 = i

Result

i^5

The imaginary unit i satisfies i^2 = -1. Its powers repeat in a cycle of four, which makes them easy to compute using remainders.

i^n repeats every 4 powers

Example: i^5 = i.

5 mod 4 = 1

Why does the cycle repeat every four powers?

Because i^4 = 1, so the pattern loops every four exponents.

Can negative exponents work?

This calculator focuses on integer exponents, but the cycle is still useful for positive powers.

Does this help with complex numbers?

Yes. Powers of i are a basic building block of complex arithmetic.

Is i the same as sqrt(-1)?

Yes. i is defined as the imaginary unit where i^2 = -1.

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