If |(z1+z2)/(z1-z2)| = 1 then Find z1/z2. Mathematics IIT JEE

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This is how I approached it. If |(z1+z2)/(z1-z2)| = 1 then (z1+z2)/(z1-z2) = either 1 or -1.

If it equal 1, then z1+z2 = z1-z2, so z2 = --z2, so Z2 = 0, meaning z1/z2 is undefined (div by zero).

If (z1+z2)/(z1-z2) = -1 then z1+z2 = -(z1-z2) = --z1 + z2, so z1 = --z1, so z1 = 0, so z1/z2 = 0.


Where did I go wrong?

simonharris