One question I need help with.

If z=cisθ = r(cosθ + isinθ), show that (1/z) = (1/r)cis(-θ)

- May 23rd 2007, 07:14 PMScontsPre-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, 03:49 AMPlato
You can use the following facts to prove it.

$\displaystyle \begin{array}{l}

z = r\left[ {cis\left( \theta \right)} \right] \\

\bar z = r\left[ {cis\left( { - \theta } \right)} \right] \\

\end{array}$

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