Find the product of (−6 −3i) and its conjugate

Question

Find the product of (−6 −3i) and it's conjugate.

Answer 1

(-6-3i)(-6+3i)

=36 - (3i)^2

=36 +9

=45

general formula is: (a+b)(a-b) = a^2-b^2

a=-6, b=3i

6 squared =36

3i squared = 9(-1) = -9

36 - -9 = 36+9 = 45

product of the sum and difference of two numbers = difference of their squares

Answer 2

The complex conjugate of z = a + bi is z* = a - bi. So the product of any complex z and its conjugate z* is

(a + bi)(a - bi) = a² + abi - abi + b² = a² + b²

So for this example, a = -6 and b = -3, so the product is 36 + 9 = 45.