How this calculation works
The sequence cycles through 1, i, −1 and −i. Adding or subtracting four from the exponent preserves the result.
THE FORMULA
iⁿ depends on n modulo 4A worked example
The least nonnegative remainder of −7 modulo 4 is 1, so i⁻⁷ = i.
Good to know
The exponent must be a whole number.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Reduce a signed exponent modulo four to evaluate an exact power of the imaginary unit.
The primary result is labeled “Power of i”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The exponent must be a whole number.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The least nonnegative remainder of −7 modulo 4 is 1, so i⁻⁷ = i.
Which rule does this calculator apply?
iⁿ depends on n modulo 4