z1,z2 and z3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center, then show that z2,z1, and z3 are in G.P
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Solution
Since Origin is the center, it is equidistant from all the three points. And |z2−z3|=|z2−z1| ... isosceles triangle. Hence z3−z0z2−z0=z2−z0z1−z0 Now z0=0 ... origin. Hence z3z2=z2z1 z22=z1z3 Hence z2 is the G.M of z1 and z3