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

1.

$z=20+0j$

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

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

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

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

2.

$z=0+12j$

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

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

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

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

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