If the real part of $\displaystyle \frac{z+1}{z-1}$ is zero, find the locus of points representing $\displaystyle z$ in the complex plane.
Any ideas on what to do first?
Since any number divided by zero is undefined and 1-1=0 (the denomitator) makes the equation undefined. Start with the real numbers on either side of it and solve the fraction. test z=0 and z=2 How far apart are they from each other? test a set of numbers closer together say z= .5 and z=1.5 (1.5 is closer to 1 than 2). Are they further apart or closer together than 0 and 2? You have 2 points on the left of zero and 2 on the right of zero so make a line to connect them and see if they ever connect.