1. ## Complex Expression #2

Write an expression for the product of a complex number c + di and its complex conjugate.

Thanks for any help!

2. Originally Posted by live_laugh_luv27
Write an expression for the product of a complex number c + di and its complex conjugate.

Thanks for any help!
Let $z=a+bi$ and $\bar{z}=a-bi$, then by the difference of squares factoring $z\cdot\bar{z}=(a+bi)(a-bi)=a^2-(bi)^2=a^2+b^2$

EDIT: Also note that $z\cdot\bar{z}=\left|z\right|^2$