Complex transformation z plane to w plane

Hi , the question and mark scheme answer to part (b) is attached
I don't understand in part (b) why the mark scheme lets z=lambda - (lambda+1) i .
Is it related to the line x+y+1=0 .

Thanks

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Originally Posted by minicooper58

I don't understand in part (b) why the mark scheme lets z=lambda - (lambda+1) i . Is it related to the line x+y+1=0 . Thanks

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Yes. Given the line in z-plane any point P on the line can be taken as or equivalently

Hi , I'm stuck after the line u/v= 2lamdba+1
I don't understand how v is multiplied by two on the next line .

Thanks