Complex Number Calculator

What this tool does

Calculate complex number instantly in your browser. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

How to use the Complex Number Calculator

1. Enter or select first number: real part a.
2. Enter or select first number: imaginary part b.
3. Enter or select second number: real part c.
4. Enter or select second number: imaginary part d.
5. Enter or select operation.
6. Read the calculated result; change any measurement to compare alternatives.

Formula

Complex numbers a + bi add component-wise and multiply with i² = −1: (a+bi)(c+di) = (ac − bd) + (ad + bc)i. Division multiplies top and bottom by the conjugate c − di. The polar form uses magnitude r = √(a² + b²) and angle θ = atan2(b, a).

a

First number: real part a

b

First number: imaginary part b

c

Second number: real part c

d

Second number: imaginary part d

op

Operation

i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Worked example

For complex number calculator, the following measurements illustrate the exact method: First number: real part a: 3; First number: imaginary part b: 2; Second number: real part c: 1; Second number: imaginary part d: -4; Operation: add.

Results explained

Result

Result from the formula above. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Real part

Real part from the formula above. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Imaginary part

Imaginary part from the formula above. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Magnitude (modulus) of result

Magnitude (modulus) of result from the formula above. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Argument of result (degrees)

Argument of result (degrees) from the formula above. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Polar form

Polar form from the formula above. i is the imaginary unit with i² = −1; every result is also given in polar (magnitude/angle) form.

Frequently asked questions