Complex Number Calculator
Perform operations on complex numbers: add, subtract, multiply, divide, find magnitude, and conjugate.
Complex Number Result
Complex Number form: a + bi, where a is the real part and b is the imaginary part.
Operations on z1 = (a + bi) and z2 = (c + di):
- Add:
(a+c) + (b+d)i - Subtract:
(a-c) + (b-d)i - Multiply:
(ac-bd) + (ad+bc)i - Divide:
((ac+bd) + (bc-ad)i) / (c² + d²)
Single-number operations:
- Magnitude:
|z| = √(a² + b²) - Conjugate:
a - bi(flip the sign of the imaginary part)
Key identities:
- i² = -1
- |z1 × z2| = |z1| × |z2|
- z × conjugate(z) = |z|²