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

1.

- wanted form =

2.

- wanted form =
- - You need to look at the graph to get this really. Using Sine or Cosine may be advisable in this situation.

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