Hey guys, was just given this question: Use the complex conjugate of z to find z^-1 when z equals 2+3i.
Okay is it asking for the inverse of the complex number, or simply to multiple it by the power of -1?
Hello, sanado!
Use the complex conjugate of $\displaystyle z$ to find $\displaystyle z^{-1}$ when $\displaystyle z \:=\:2+3i.$
We have: .$\displaystyle z^{-1} \;=\;\frac{1}{2+3i}$
The conjugate of $\displaystyle 2 + 3i$ is $\displaystyle 2 - 3i$
Multiply top and bottom by the conjugate:
. . $\displaystyle \frac{1}{2+3i}\cdot\frac{2-3i}{2-3i} \;=\;\frac{2-3i}{4 -6i + 6i - (3i)^2} \;=\;\frac{2-3i}{13} \;=\;\frac{2}{13} - \frac{3}{13}i $