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Modulus and Argument OCR FP1

I know the answer to the question but do not understand it, please help:

Use an argand diagram to find, in form a+bi, the complex number that satisfies,
1) arg(z+2i)=1/6pi, arg(z-2i)=-1/3pi
2) arg(z-2)=3/4pi, |z+2|=3

I have drawn diagram for both, I understand it's the intersection points but I don't know how to work out the intersection point, where are the simultaneous equations?!
Reply 1
Draw two triangles and create equations using inverse tan.

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