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.
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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.