Complex Number to Polar & Exponential Forms Calculator with Steps

z = a + i b → polar & exponential

Enter real (a) and imaginary (b). See step‑by‑step calculation of modulus r and argument θ.

General formulas:

\[ z = a + i b \quad \Longrightarrow \quad r = \sqrt{a^2 + b^2}, \quad \theta = \arg(z) \]

with \( -\pi < \theta \le \pi \) (principal value). Then:

\[ \text{Polar: } z = r\big(\cos\theta + i\sin\theta\big) \] \[ \text{Exponential: } z = r e^{i\theta} \]

Enter complex number

Real part (a)

Imaginary part (b)

Decimal places:

Modulus r —

🔹 Radians

Argument θ — rad

Polar form —

Exponential

🔸 Degrees

Argument θ — °

Polar form —

Exponential

* Principal argument: -π < θ ≤ π (-180° < θ ≤ 180°).