Write the product of 2-4i and it's conjugate in the form of a+bi

Question

Where a and b are real numbers

Answer 1

The conjugate of the given complex number is    2 + 4i.    This conjugate was obtained by using a quadratic formula to solve an arbitrary quadratic equation.

 

 

So the product of the given complex number and the conjugate is

 

(2 - 4i)(2 + 4i) = 4 - 16i²

 

 

Knowing that  i²=-1,

 

 4 - 16(-1) = 4 + 16

                = 20

 

In the form of   a+bi, that will be     20 + 0i.