Perform operations with complex numbers including addition, multiplication, division, and finding conjugates. Free online complex number calculator.
Perform complex number operations with our free online calculator. Add, subtract, multiply, divide complex numbers, find conjugates, and calculate magnitudes.
Enter complex numbers above to see the calculation result.
Complex numbers are written as a + bi where a is the real part and b is the imaginary part.
The imaginary unit i satisfies i² = -1, which allows us to work with square roots of negative numbers.
The conjugate of a + bi is a - bi. It's useful for division and finding magnitudes.
The magnitude (modulus) of a + bi is √(a² + b²), representing the distance from the origin.
(3 + 4i) + (1 + 2i) = 4 + 6i
(3 + 4i) × (1 + 2i) = -5 + 10i
Conjugate of 3 + 4i = 3 - 4i
|3 + 4i| = 5
A complex number is a number in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit (i² = -1).
To add complex numbers, add the real parts and imaginary parts separately: (a + bi) + (c + di) = (a + c) + (b + d)i
The conjugate of a + bi is a - bi. It's useful for division and finding the magnitude of complex numbers.