Complex Number Calculator | Rectangular & Polar

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, log2, and log10)
  • 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).

Number Format
Notation | Output
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What is a complex number?