Complex Number Calculator
Enter two complex numbers and get their sum, difference, product, quotient, modulus and argument instantly — a fast study aid for engineering and algebra students working with the imaginary unit i in a + bi form.
How to use
- Enter the parts of z1 = a + bi and z2 = c + di.
- For a negative imaginary part, enter a minus value.
- Add, subtract, multiply, divide, modulus and argument will all be shown.
Note: In multiplication i^2 = -1 applies: (a+bi)(c+di) = (ac - bd) + (ad + bc)i. For division, the denominator is rationalized with the conjugate.
Tips
- Enter a negative imaginary part with a minus sign, e.g. c = 3, d = -4.
- Remember i squared = -1 when multiplying — the tool applies it automatically.
- Modulus |z| gives the distance from the origin; argument gives the angle.
- For division the denominator is rationalized with its conjugate — watch the steps.
Frequently Asked Questions (FAQ)
What operations are supported?
Adding, subtracting, multiplying and dividing complex numbers, plus finding the modulus.
What do I enter?
The real and imaginary parts of z1 equals a plus bi and z2 equals c plus di. Type a negative number in the imaginary field for a negative imaginary part.
Does it show the argument too?
Yes. Besides the sum, difference, product, quotient and modulus, the tool also shows the argument of each complex number.
How is complex division calculated?
The denominator is rationalized with its conjugate, which keeps the result in a plus bi form.