Easily calculate **real** and **imaginary numbers** with this free online **complex number calculator**.

This calculator can handle **complex numbers** in any form, and converts between **rectangular** ** a+bi** and

**polar**

**forms of complex numbers.**

`r∠(θ)`

As a powerful **scientific complex number calculator**, it can handle a wide range of mathematical expressions, from simple forms like (1+2i) - (3-4i) to any complicated forms like sin(1+2i)/ln(3+4i) + atan(1+3i) - 4∠(1.8).

By selecting the **Show work** checkbox, the **real & imaginary number calculator** provides **step-by-step** solutions.

The **complex number calculator** performs conversions between rectangular and polar forms internally. By selecting the **Convert results to all forms** checkbox, you can display the results in **rectangular** (**standard**), **polar** (**phasor**), and other **modular** forms.

## Powerful Features for Calculation on Complex Numbers

This **real and imaginary number calculator** provides the following functionalities.

### Basic Operations

Perform basic operations – **addition**, **subtraction**, **multiplication**, and **division** – on **complex numbers**.

### Powers and Roots

Calculate **powers** and *principal* **roots** of complex numbers.

### Advanced Mathematical Operations

Calculate expressions involving **trigonometric**, **hyperbolic**, **exponential**, and **logarithmic** functions that have **real**, **imaginary**, or **complex numbers** as *arguments*.

### Special Function Evaluation

Evaluate functions like ** Γ()**,

**, and**

`ψ()`

**, corresponding to the**

`ζ()`

**Gamma**,

**psi**, and

**zeta**functions, respectively.