Algebra & Equations

Complex Power (De Moivre)

Raise a complex number to an integer power.

Formula

Formula
rn(cos nθ + i sin nθ)

Variables

SymbolDefinitionType & rangeUnitsRole
a, b complex number real number (ℝ) real input
n integer exponent integer (ℤ) input

Try it yourself

Interactive calculator
Result

Worked examples

Example 1
Givena (real) = 1, b (imag) = 1, n = 4
Result-4.000000000000001 + 4.898587196589414e-16i
Example 2
Givena (real) = 0, b (imag) = 1, n = 2
Result-1 + 1.2246467991473532e-16i