# Complex numbers! Elementary problem *Quick help needed*

• Sep 21st 2009, 12:37 PM
Hanga
Complex 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 PM
Plato
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 PM
Hanga
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 PM
Plato
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\$.