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

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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 }))