Find the product of -4-3i and its conjugate. The answer is a+bi where

Question

the real number a equals

the real number b equals

 

Answer 1

The conjugate of -4-3i    is   -4+3i.   Think of these complex numbers as solutions when using the quadratic formula.

 

 

(-4 - 3i)(-4 + 3i) = 16 - 9i²

 

                         = 16 - 9(-1)

 

                         = 16 + 9

 

                         = 25

 

The real number a is 25.  Since there is no imaginary number, the value of b is zero .

 

The product is then      25 + 0i

 

Answer 2

(-4+3i)(-4-3i) = (-4)² - (3i)² = 16 + 9 = 25

 

                                                     = 25 + 0i