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Complex Number Calculator — convert, operate, and show steps

Convert between a+bi and r∠θ, run complex operations, see integer powers and every n-th root, and follow an Argand plot that updates with each step.

שפות נוספות: ja | en | es | zh-CN

How to use (3 steps)

  1. Select the mode: Convert, Operations, Power, or Roots.
  2. Enter z (and w or n if needed), choosing rectangular a+bi or polar r∠θ.
  3. Tap Compute to see the result, steps, and Argand plot. Copy URL shares the exact setup.

A sample z = 1 + i is preloaded and computed automatically on first view.

Angle & precision
Unit
Angle range
0–12 decimal places
Mode
Operand z

Results

Rectangular (a + bi)
—
Polar (r ∠ θ)
—

How it's calculated

    Argand plot

    Vectors for z, w, and the highlighted result or roots update after each computation.

    Teacher notes

    Toggle reminders about principal values, multi-valued roots, and rounding behaviour.

    FAQ

    Which operations does this complex number calculator cover?

    It converts between rectangular and polar form, performs addition, subtraction, multiplication, division, integer powers, and lists every n-th root with narrated steps.

    How can the Argand plot help me learn?

    It draws vectors for your inputs and highlights the result or each root so you can see magnitude and angle changes at a glance.

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