Question

Find the product of the complex number and its conjugate.

3 + 3i

Answer 1

The complex conjugate of a+bi is a - bi. The product of a complex number and its conjugate will be \[(a+bi)(a-bi)=a^2-abi+abi+b^2i^2=a^2-b^2\]

Answer 2

9 - 9i?

Answer 3

Sorry, I made a sign mistake, that should be
\[(a+bi)(a-bi)= a^2-abi+abi-b^2i^2=a^2+b^2\]

Answer 4

So you have a = 3, b = 3, and the result is 3^2+3^2=18

Answer 5

the i terms cancel out, and the i^2 term just changes sign because i^2= -1