Math & Statistics
De Moivre's Theorem Calculator
Raise a complex number to a power using De Moivre's theorem.
Your inputs
Change any value to update the result instantly.
Result real part
-2.0000 + 2.0000i
Result imaginary part
2
Modulus r
1.4142
Angle θ
45 °
Formula and working
(r cis θ)ⁿ = rⁿ cis(nθ)
- 1
Substitute your values
Real part = 1; Imaginary part = 1; Power n = 3
- 2
Apply the formula
(r cis θ)ⁿ = rⁿ cis(nθ) = -2.0000 + 2.0000i
Frequently asked questions
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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