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Complex Number Calculator

Add, subtract, multiply, divide and find modulus, argument, conjugate, powers and roots of complex numbers.

Z1 = a + bi
3 + 4i = 5 ∠ 53.130102°
Z2 = c + di
1 - 2i = 2.236068 ∠ -63.434949°

integer powers −12…12

Z1 + Z24 + 2i (4.472136 ∠ 26.565051°)
Z1 − Z22 + 6i (6.324555 ∠ 71.565051°)
Z1 × Z211 - 2i (11.18034 ∠ -10.304846°)
Z1 ÷ Z2-1 + 2i (2.236068 ∠ 116.565051°)
|Z1| (modulus)5
arg(Z1) (degrees)53.130102°
conj(Z1)3 - 4i
Z12-7 + 24i
√Z1 (principal root)2 + i
Z2 polar2.236068 ∠ -63.434949°

Division multiplies numerator and denominator by the conjugate of Z2. Polar form: r∠θ with r = |z| and θ = atan2(im, re). The principal square root always returns the root with a non-negative real part.

About Complex Number Calculator

Add, subtract, multiply, divide and find modulus, argument, conjugate, powers and roots of complex numbers.

Complex Number Calculator applies the standard formula for this calculation and returns a clean, readable result — no spreadsheet setup or manual working required.

How to Use Complex Number Calculator

  1. Enter your numbers in the input fields shown above.
  2. Choose any options (units, rounding, precision) if the tool offers them.
  3. The result updates automatically — no button needed.
  4. Copy the answer or reset the fields to start a new calculation.

Key Features

  • Instant results with a clear, readable output format.
  • Handles decimals, percentages and large numbers cleanly.
  • Fast and private — every calculation runs on your device.

Frequently Asked Questions

What formula does Complex Number Calculator use?

Complex Number Calculator uses the standard, widely accepted formula for this calculation. Results are rounded only for display, so they are reliable for homework, planning and quick checks.

Is Complex Number Calculator free to use?

Yes. Complex Number Calculator is completely free with unlimited use — no account, download or payment required.

Is my data uploaded to a server?

No. Complex Number Calculator runs entirely in your browser. Your inputs are never sent to our servers or stored anywhere.

Does Complex Number Calculator work on mobile?

Yes. The interface is fully responsive and works in any modern browser on Android, iPhone, tablets and desktops.

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