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

< A-level Mathematics‎ | MEI‎ | FP1‎ | Complex Numbers

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