A **complex number calculator** (aka **imaginary number calculator**) is a **scientific calculator** that is also capable of performing
mathematical operations and function evaluations with **imaginary numbers**, and in general, complex numbers.

In addition to performing the four basic operations of **addition**, **subtraction**, **multiplication** and **division** of complex numbers, this **complex number calculator** can be used to calculate **powers** and *principal* **roots** of **complex numbers**.

As a powerful **scientific complex number calculator** it can also be used to calculate **exponential**, **logarithmic**, **trigonometric**, **hyperbolic**, **Γ** (**Gamma**), **ψ** (**psi**) and **ζ** (**zeta**) functions with **imaginary** or **complex number** as arguments.

**Complex numbers** can be entered in the **rectangular** (standard) form **a + bi**, where a and b are the **real part** and **imaginary part**, respectively.

**Complex numbers** can also be entered in the **polar** form **r∠ θ**, where r is the *signed* **module** (or *length*) and θ is the **argument** (or *angle*) of the **complex number**.

Furthermore, this **complex number calculator** shows work step-by-step and converts the complex number results to **standard**, **polar** and other **modular** forms.

For instance, this **imaginary / complex number calculator** easily computes mathematical expressions containing **complex numbers** from the simplest forms such as
(1+2i)-(3-4i),
to arbitrary complicated forms such as
sin(1+2i) / ln(3+4i) + atan(1+3i) − 4∠(1.8), which contains *non-algebraic* functions and **complex numbers** in **rectangular and polar forms**.