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For complex numbers z and q, prove that |z| 2 w – |w| 2 z = z – w if and only if z = w or z w - = 1.

 For complex numbers z and q, prove that |z|2 w – |w|2 z = z – w if and only if z = w or z w = 1. 

Grade:11

1 Answers

mycroft holmes
272 Points
12 years ago

Rewrite the equation as 

 

If   then the equation trivially holds. If , then taking modulus on both sides, we obtain 

 

.

 

Now we can rewrite the equation as 

 

which yields 

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