Calculate complex number

Perform arithmetic on two complex numbers and show each result’s magnitude and phase.

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ToolComplex Number Calculator
Input
Output
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Preview

How it works

Arithmetic operates on real and imaginary components using i² = −1. Modulus is √(a²+b²), and argument uses atan2(imaginary, real) before conversion from radians to degrees.

  • Rectangular form is the primary result; modulus and argument are derived views.
  • Division rejects a zero complex denominator.

Worked example

(1 + 2i) times (3 + 4i)
Multiplying two complex numbers
Input
											Real a: 1
Imaginary a: 2
Real b: 3
Imaginary b: 4
Operation: multiply
Output
												Real part: -5
Imaginary part: 10
Result display: -5 + 10i
Modulus: 11.1803
Argument degrees: 116.5651
Argument radians: 2.0344
Polar form: 11.1803 at 116.5651 degrees

When to use this

AC-circuit exercises add impedances, signal-processing lessons convert samples to magnitude and phase, and quadratic solvers inspect imaginary roots.

Edge cases

  • Dividing by 0+0i is rejected rather than producing infinities.
  • A negative imaginary component is rendered with a minus sign, not “+ -bi”.
  • The argument of a negative real number follows atan2’s signed-zero and branch convention.

References