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Um... this may be just me but when your finding the locus of w, z, x etc. the imaginary and real axis don't apply. Which means that rawrence is still correct. What I mean to say is that the locus will never the Re, x or Im, y axis. Am I making any sense?

Use the fact that sin(a)=cos(pi/2-a) and vice versa. i.e cos(a)=sin(pi/2-a) EDIT:Go with Rawrence's answer as the method I and hscishard posted will get you no where (just tried it)