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

Question image for Sir can you tell me the solution of this complex n
Profile image of Aditya Dev
9 Years agoGrade Select Grade
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2 Answers

Profile image of Vikas TU
9 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.
Profile image of mycroft holmes
ApprovedApproved Tutor Answer9 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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