Prove that if Z1 and Z2 are complex numbers, and |z1| = |z2| = 1, z1*z2 = -1 then (Z1*Z2)/(1+Z1Z2) is real number.
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Are Z1 and Z2 the same as z1 and z2? If so then, since you require that z1z2= -1, z1z2/(1+ z1z2)= -1/(1- 1) which is not defined. I strongly suspect that was not what you intended to say.