# Multiplication of complex numbers Multiplication of complex numbers

The complex number is written in the form z = a+ bi.

We need to determine the result of the product of two complex numbers.

Let z1= a+ bi

and z2 = c+di

Now we need to calculate the product of z1*z2.

==> z1*z2= (a+bi)(c+di)

We will expand the brackets.

==> z1*z2= (a*c + bc*i + ad*i + bd*i^2)

Now we know that i^2 = -1

==> z1*z2= ac + bc*i + ad*i - bd )

Now we will combine real terms and complex terms together.

==> z1*z2= (ac-bd) + (bc+ad)*i

Now I will give an example:

Find the product of ( 2-3i) * ( 3+ 5i)

Let us expand.

==> (2*3 - 3*3*i + 2*5i -3i*5i

==> (6 - 9i + 10i - 15i^2)

i^2 = -1

==> (6 + i -15) = (-9 + i)

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