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Complex numbers
Complex numbers: formula, units and explained result. No account required. Processing stays in your browser.
z = a + bi; |z| = √(a²+b²); arg(z) = atan2(b,a)
Modulus, principal argument and conjugate. The argument of zero is undefined.
How to use this calculator
- Identify the quantities and convert them to the units shown.
- Apply the formula first, then compare with the substitution and result.
- Check the assumptions and whether the order of magnitude makes sense.
Levels are approximate topic groupings, not a complete curriculum for every country. Numerical results are rounded and may lose precision for extreme or nearly singular inputs.
A practical example
Use these sample inputs to check the calculation before entering your own values.
- Real part a
- 3
- Imaginary part b
- 4
Result for this example
- Modulus
- 5
- Argument
- 53.13010235415598 °
- Conjugate
- 3 − 4i