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Difficult complex geometry q (1 Viewer)
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Can you show us what you tried first for part ii. Just give it go.
Did the sample solution not help?
I would recommend finding the modulus and the argument separately.
For the modulus you would use pythag
Given that since OB is a tangent to the circle
+(R-r)^2}\ \text{pythag again as}\ CO^2=CA^2+OA^2\\OD=\sqrt{(R^2-r^2)+(R-r)^2}\\OD=\sqrt{R^2-r^2+R^2-2Rr+r^2}\\OD=\sqrt{2R^2-2Rr})
Which is the modulus of D
Now to find the argument, we have to use the triangle COD which is a Isosceles triangle cause CO=CD as they are both the radius of the same circle.
Therefore the angle between line OD and the positive real axis would be
cause it is complementary to 
Hence the complex number represented by D would be
For the modulus you would use pythag
Now to find the argument, we have to use the triangle COD which is a Isosceles triangle cause CO=CD as they are both the radius of the same circle.
Therefore the angle between line OD and the positive real axis would be
Hence the complex number represented by D would be