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.
Tushar Singh , 15 Years ago
Grade 11
Algebra> complex numbers...
1 Answersmycroft holmes
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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