# Math Help - Simply Complex numbers

1. ## Simply Complex numbers

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?

2. $z^{ - 1} = \frac{1}
{z} = \frac{{z^* }}
{{zz^* }} = \frac{{z^* }}
{{|z|}}$

Use the complex conjugate of $z$ to find $z^{-1}$ when $z \:=\:2+3i.$

We have: . $z^{-1} \;=\;\frac{1}{2+3i}$

The conjugate of $2 + 3i$ is $2 - 3i$

Multiply top and bottom by the conjugate:

. . $\frac{1}{2+3i}\cdot\frac{2-3i}{2-3i} \;=\;\frac{2-3i}{4 -6i + 6i - (3i)^2} \;=\;\frac{2-3i}{13} \;=\;\frac{2}{13} - \frac{3}{13}i$