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

1.

$z=20+0j$

wanted form = $z=r(cos\theta +jsin\theta )$

$r={\sqrt {20^{2}+0^{2}}}=20$

$tan({0 \over 20})=0$

$z=20(cos(0)+jsin(0))$

2.

$z=0+12j$

wanted form = $z=r(cos\theta +jsin\theta )$

$r={\sqrt {(}}{0^{2}+12^{2}})=12$

$tan({12em \over 0})=\infty$

$tan^{-1}(\infty )={\pi \over 2}$ - You need to look at the graph to get this really. Using Sine or Cosine may be advisable in this situation.

$z=12(cos({\pi \over 2})+jsin({\pi \over 2}))$