Edexcel FP2 complex transformations

I just spent quite a while trying to do that through real and imaginary parts but I've done it now and hopefully can be of assistance

Basically you need to manipulate the algebra to get (z - 2i)/(z + 2) in terms of z. This is best done by first rearranging to find z. After some fractional manipulation to reach that you should have it equal to a very nicely simplified w function, whose argument naturally must be pi/2. Or is your problem with doing said algebraic working/interpreting the final function to sketch it?

I could see that was what the end goal was, but didn't see how they got there. I understand where the (z-2i) comes from, but not the (z+2) after the rearranging. I'm just having one of those days...

post the question please

Had a weird problem with putting it directly into a post, the link is in the OP.

Sorry but I am scared of viruses ...besides the whole point of being here is not to go to a third party site if we can help it.

Well, it worked now, thankfully

which part?

Part c. I can do the other two, but don't quite understand how they've rearranged the the transformation for (z-2i)/(z+2) from that alone.

it can be done in two ways that I can think of

Try this
solve the transformation for z
subtract 1 + i (centre of arc in previous part)
mod both sides
LHS =root2 (radius of the arc in previous part)
RHS set w = u+ iv
....finish off

Thank you. I'll have an attempt tomorrow. The mark scheme was incredibly sparse and didn't mention any alternative methods in detail.

Part c. I can do the other two, but don't quite understand how they've rearranged the the transformation for (z-2i)/(z+2) from that alone.