Complex Number Calculator

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OperationAdd (+)Subtract (-)Multiply (×)Divide (÷)Power z^n (De Moivre)Conjugate (single number)Modulus and Argument only

Angle unit for outputDegrees (°)Radians (rad)

Imaginary unit symboli (mathematics)j (electrical engineering)

Real part of z1 (a)

Imaginary part of z1 (b)

Real part of z2 (c)

Imaginary part of z2 (d)

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Result (rectangular a+bi)

11 - 10i

Modulus |z|14.866069

Argument (angle)-42.2737°

Polar (phasor) form14.8661 ∠ -42.2737°

Exponential form14.8661 · e^(-0.7378i)

Trigonometric (CIS) form14.8661(cos -42.2737° + i sin -42.2737°)

Conjugate of result11 + 10i

Modulus of z13.605551

Argument of z133.6901°

Modulus of z13.605551

Modulus of result14.866069

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Multiplication: 11 - 10i.

• The modulus is 14.8661, the distance from the origin on the complex plane.
• The argument is -42.2737°, the angle from the positive real axis.
• Multiplication in polar form: multiply the moduli and add the arguments. The rectangular formula uses (ac - bd) + (ad + bc)i.
• Polar form: 14.8661 ∠ -42.2737°. Exponential form: 14.8661 · e^(-0.7378i).

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