Hi! Can someone please solve the below problem?
Find all complex numbers such that $|z-1|=|z+3|=|z-i|$
Express each answer in the form $a+bi$, where $a$ and $b$ are real numbers.
Finish solving this.
I only got one answer but maybe there are more.
\(|z-1|=|z+3|=|z-i|\\ |a+bi-1|=|a+bi+3|=|a+bi-i|\\ |(a-1)+bi|=|(a+3)+bi|=|a+(b-1)i|\\ (a-1)^2+b^2=(a+3)^2+b^2=a^2+(b-1)^2\\ (a-1)^2+b^2=(a+3)^2+b^2=a^2+(b-1)^2\\ etc \)
+5 
