Explore our free online **complex number calculator**, also known as an *imaginary number calculator*. This powerful **scientific calculator** with user-friendly features can evaluate and simplify mathematical expressions containing **real** and **imaginary numbers** in any form including **rectangular** (**standard**) ** a+bi** and

**polar**(

**phasor**)

**. It converts and shows the results in standard and various modular forms such as polar.**

`r∠(θ)`

## Powerful Features for Calculation on Complex Numbers

This comprehensive **complex number calculator** can handle complex number expressions ranging from simple forms like (1+2i) - (3-4i) to complicated forms like sin(1+2i)/ln(3+4i) + atan(1+3i) - 4∠(1.8).
The calculator provides **step-by-step** solutions and 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.

## Seamless Rectangular and Polar Conversion

The **complex number calculator** performs **conversions between rectangular and polar forms** internally, and can display the results in various forms, including **rectangular** (**standard**) ** a+bi** and

**polar**(

**phasor**)

**, and other**

`r∠(θ)`

**modular**forms.