# A-level Mathematics/MEI/FP1/Complex Numbers/argand diagram answers

1.

${\displaystyle z=20+0j}$
wanted form = ${\displaystyle z=r(cos\theta +jsin\theta )}$
${\displaystyle r={\sqrt {20^{2}+0^{2}}}=20}$
${\displaystyle tan({0 \over 20})=0}$
${\displaystyle z=20(cos(0)+jsin(0))}$

2.

${\displaystyle z=0+12j}$
wanted form = ${\displaystyle z=r(cos\theta +jsin\theta )}$
${\displaystyle r={\sqrt {(}}{0^{2}+12^{2}})=12}$
${\displaystyle tan({12em \over 0})=\infty }$
${\displaystyle tan^{-1}(\infty )={\pi \over 2}}$ - You need to look at the graph to get this really. Using Sine or Cosine may be advisable in this situation.
${\displaystyle z=12(cos({\pi \over 2})+jsin({\pi \over 2}))}$