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Polar Form of Complex Numbers Calculator

Online polar form: from the real and imaginary parts get the modulus r and argument θ.

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z=r(cosθ+i sinθ)
z=a+bi
a
b

📖 Tutorial | Polar Form

1. Definition
The trigonometric (polar) form is z=r(cosθ+i sinθ), with r=|z| and argument θ.
2. Formula & Notation
r,θModulus, argument
3. Properties & Laws
  • r=√(a²+b²);
  • θ=atan2(b,a);
  • a=r cosθ, b=r sinθ;
  • Zero has no argument.
4. Steps
  1. Enter a,b;
  2. Click "To Polar";
  3. Or click "Load Example".
5. Worked Examples
Example: 1+i: r=√2, θ=45, √2(cos45+i sin45).
6. Common Pitfalls
Use atan2;
Zero special;
Angles in degrees.

❓ FAQ | Polar Form

Form?
r(cosθ+i sinθ).
Argument?
atan2.
r?
Modulus.
Parts?
r cosθ.
Example?
√2, 45.
Principal?
−180 to 180.