Our online **complex number calculator** is a powerful and easy-to-use *scientific calculator* for performing mathematical **operations** and **evaluating functions** with **real** and **imaginary numbers**, and **complex numbers** in general.

The **complex number calculator** supports both **rectangular** (**a + bi**) and **polar** (**r∠(θ)**) forms of **complex numbers**, and **converts** between the two forms. It shows you the **work step-by-step** and also displays the result of calculations to various forms, including **rectangular** (**standard**), **polar**, and **modular** forms.
Instruction

Here is a summary of some of the capabilities that our *real* and **imaginary number calculator** can perform:

- Addition, subtraction, multiplication, and division of complex numbers
- Conversion between rectangular and polar forms of complex numbers
- Calculation of powers and roots of complex numbers
- Evaluation of trigonometric functions of complex numbers (sine, cosine, tangent, cotangent, secant, and cosecant)
- Evaluation of hyperbolic functions of complex numbers (sinh, cosh, tanh, cotanh, sech, and csch)
- Evaluation of exponential and logarithmic functions of complex numbers (exp, ln, log
_{2}, and log_{10}) - Evaluation of the Gamma function of complex numbers (Γ)
- Evaluation of the Psi function of complex numbers (ψ)
- Evaluation of the Zeta function of complex numbers (ζ)

This calculator is a fully-developed *scientific* **complex number calculator** that can handle **complex number expressions** from basic arithmatic to advanced mathematical operations. It can easily compute expressions of **complex numbers**, from simple forms like (1+2i) - (3-4i) to more complicated forms like sin(1+2i) / ln(3+4i) + atan(1+3i) - 4∠(1.8).