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Sir can you tell me the solution of this complex number question in the attachment? The answer is A,D

Sir can you tell me the solution of this complex number question in the attachment? The answer is A,D

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2 Answers

Vikas TU
14149 Points
4 years ago
put z1 = x1 +iy1
and'z2 = x2 + iy2
simple and also thiss is given as:
(x1)^2 + (y1)^2 = (x2)^2 + (y2)^2.
Us ethis info.
mycroft holmes
272 Points
4 years ago
Several ways to approach this:
 
  1. Write z = \frac{z_1+z_2}{z_1-z_2} = \frac{1 + \alpha}{1 - \alpha} where \alpha = \frac{z_2}{z_1}
So 
 
\overline {z} = \frac{1+\overline {\alpha} } {1-\overline {\alpha} } = \frac{1+\frac{1} {\alpha} } {1- \frac{1} {\alpha}} 
 
since |\alpha| =1 \Rightarrow \overline{\alpha} = \frac{1}\alpha
 
Hence \overline{z} = \frac{1+\alpha}{\alpha-1} = -z
 
So either z is purely imaginary or z=0. (z=0 is possible when z1=-z2 which is permitted with the restrictions mentioned in the problem)
 
 

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