A complex number is a number consist of real part and imaginary part and is represented as a + bi. In a complex number, the Real part and Imaginary parts are denoted by Re(z) and Im(z).
a is a real part
b is a complex part
In complex number multiplication calculator simple multiplication operation is performed.
Let z1 and z2 be the two complex numbers
z1 = a + bi
z2 = c + di
Complex Numbers Multiplication Formula:
z1.z2 = (a + bi).(c + di)
= ac + adi + bci +bdi2
but remember i2 = -1,
So z1.z2 = (ac - bd) + (bc + ad)i
Perform Complex Multiplication for the below numbers
X = 1 + 2i, Y = 3 + 4i
Here a = 1, b = 2, c = 3, d = 4
The result is,
z1.z2 = ( 1*3 - 2*4 ) + ( 2*3 + 1*4 )i
= -5 + 10i
The resultant complex value is -5 + 10i
When you try such calculations on your own, this complex number multiplication calculator can be used to verify results of calculations.