Pre-Calc Graphing with Complex numbers. Multiplying with complex numbers.

• May 23rd 2007, 08:14 PM
Sconts
Pre-Calc Graphing with Complex numbers. Multiplying with complex numbers.
One question I need help with.

If z=cisθ = r(cosθ + isinθ), show that (1/z) = (1/r)cis(-θ)
• May 24th 2007, 04:49 AM
Plato
You can use the following facts to prove it.
$\begin{array}{l}
z = r\left[ {cis\left( \theta \right)} \right] \\
\bar z = r\left[ {cis\left( { - \theta } \right)} \right] \\
\end{array}$

$\frac{1}{z} = \frac{{\bar z}}{{\left| z \right|^2 }}$