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

1.
 * $$ z = 20 + 0j $$
 * wanted form = $$ z = r(cos \theta + j sin \theta)$$
 * $$ r = \sqrt{20^2 + 0^2} = 20 $$
 * $$ tan( {0 \over 20}) = 0 $$
 * $$ z = 20(cos(0)+jsin(0)) $$

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