Polar Form Calculator

Use our free polar form calculator to convert rectangular complex numbers to polar form z = r·e^(iθ), convert polar to rectangular, and compute powers using De Moivre's theorem.

Math

Mode

z =

Modulus r

Argument θ (radians)

Power n

Formula

Convert complex numbers between rectangular (a+bi) and polar (r·e^(iθ) or r·(cosθ+i·sinθ)) forms. Also apply De Moivre's theorem to compute powers zⁿ.

z = r·e^(iθ) = r·(cos θ + i·sin θ), De Moivre: zⁿ = rⁿ·e^(i·nθ)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select mode: Rect→Polar, Polar→Rect, or De Moivre.
2For Rect→Polar: enter z as a+bi.
3For Polar→Rect: enter r and θ in radians.
4For De Moivre: enter z and power n.
5Click Calculate.

Examples

3+4i to polar

1.r = √(3²+4²) = 5
2.θ = atan2(4,3) = 0.9273 rad (53.13°)

Result: 5

(1+i)³ using De Moivre

1.r = √2, θ = π/4
2.r³ = 2√2, 3θ = 3π/4
3.Result = 2√2·(cos(3π/4)+i·sin(3π/4)) = −2+2i

Result: 2.8284271247

Frequently Asked Questions

z = r·e^(iθ) where r = |z| is the modulus and θ = arg(z) is the argument.

r = √(a²+b²), θ = atan2(b,a).

(r·e^(iθ))ⁿ = rⁿ·e^(i·nθ) — used to compute powers of complex numbers.

Enter θ in radians. The calculator also shows degrees for reference.

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CalculateMe Team

Last updated: 2026-07-15

Polar Form Calculator

Formula

How It Works

Examples

3+4i to polar

(1+i)³ using De Moivre

Frequently Asked Questions

What is polar form?

How do I convert to polar?

What is De Moivre's theorem?

Can I use degrees?

Related Calculators

Polar Form Calculator

Formula

How It Works

Examples

3+4i to polar

(1+i)³ using De Moivre

Frequently Asked Questions

What is polar form?

How do I convert to polar?

What is De Moivre's theorem?

Can I use degrees?

Related Calculators