Write an expression for the product of a complex number c + di and its complex conjugate.
Thanks for any help!
Let $\displaystyle z=a+bi$ and $\displaystyle \bar{z}=a-bi$, then by the difference of squares factoring $\displaystyle z\cdot\bar{z}=(a+bi)(a-bi)=a^2-(bi)^2=a^2+b^2$
EDIT: Also note that $\displaystyle z\cdot\bar{z}=\left|z\right|^2$
Last edited by Mathstud28; Nov 19th 2008 at 04:03 PM.
Reason: Edit