So im stuck at;

Find the complex numbers with abs 1 for which it works that:

|1-zi|=1

How do I solve it? I've tried almost everything I can use and do, the problem is I don't know where to start.

I've tried setting

z=a+bi

|1-zi|=1 as z(roof)

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- Sep 21st 2009, 12:37 PMHangaComplex numbers! Elementary problem *Quick help needed*
So im stuck at;

Find the complex numbers with abs 1 for which it works that:

|1-zi|=1

How do I solve it? I've tried almost everything I can use and do, the problem is I don't know where to start.

I've tried setting

z=a+bi

|1-zi|=1 as z(roof) - Sep 21st 2009, 01:18 PMPlato
This is the same as $\displaystyle |(1+y)-xi|=1$ or $\displaystyle (1+y)^2+x^2=1$.

That is a circle of points in the complex plane with center $\displaystyle -i$ with radius 1. - Sep 21st 2009, 01:25 PMHanga
Yeah I tried it, and it does not work. Well atleast it's not the same as the answer im supposed to get which is;

(+-)sqr(3)/2 - i/2

I understand exactly how you think, thought for me it's the Z part of |1-zi|=1 which ruins every and all attempts for me to crack this problem. - Sep 21st 2009, 01:31 PMPlato
Well if you want the abolute value to be 1, solve these two.

$\displaystyle (1+y)^2+x^2=1$ & $\displaystyle x^2+y^2=1$.