Algebra & Equations
Complex Power (De Moivre)
Raise a complex number to an integer power.
Formula
Formula
rn(cos nθ + i sin nθ)
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| a, b | complex number | real number (ℝ) | real | input |
| n | integer exponent | integer (ℤ) | — | input |
Try it yourself
Interactive calculator
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