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De Moivre's Theorem Calculator

Online De Moivre's tool: raise a polar-form complex number to n; modulus powers and argument multiplies.

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[r(cosθ+i sinθ)]ⁿ=rⁿ(cos nθ+i sin nθ)
Modulus
Angle
Integer

📖 Tutorial | De Moivre's

1. Definition
De Moivre's formula: [r(cosθ+i sinθ)]ⁿ=rⁿ(cos nθ+i sin nθ).
2. Formula & Notation
r,nModulus, power
3. Properties & Laws
  • Modulus rⁿ;
  • Argument nθ;
  • For r=1, (cosθ+i sinθ)ⁿ=cos nθ+i sin nθ;
  • Negative n works.
4. Steps
  1. Enter r,θ,n;
  2. Click "Power";
  3. Or click "Load Example".
5. Worked Examples
Example: (cos30+i sin30)³: cos90+i sin90=i.
6. Common Pitfalls
Argument × n;
Modulus also powers;
Degrees.

❓ FAQ | De Moivre's

Formula?
Power, ×n.
Use?
Powers.
r=1?
cos nθ.
Negative?
Works.
Example?
i.
n=0?
1.