Complex Number Calculator
Perform addition, subtraction, multiplication, and division of complex numbers.
First Complex Number (z1)
+
i
z1 = 3.0000 + 4.0000i
Second Complex Number (z2)
+
i
z2 = 1.0000 + 2.0000i
Operation
Properties of z1
Magnitude |z1|5.000000
Argument (radians)0.927295
Argument (degrees)53.13
Conjugate z1*3.0000 - 4.0000i
(3.0000 + 4.0000i) + (1.0000 + 2.0000i)
4.0000 + 6.0000i
+z1 + z2
4.0000 + 6.0000i
-z1 - z2
2.0000 + 2.0000i
xz1 x z2
-5.0000 + 10.0000i
/z1 / z2
2.2000 - 0.4000i
Polar Form of z1
5.0000 x (cos(53.13) + i sin(53.13))
= 5.0000 x e^(i x 0.9273)
Complex Plane
z1 z2 Result
Complex Number Formulas
Addition
(a+bi)+(c+di) = (a+c)+(b+d)i
Multiplication
(a+bi)(c+di) = (ac-bd)+(ad+bc)i
Magnitude
|a+bi| = sqrt(a^2+b^2)
Conjugate
(a+bi)* = a-bi