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Sir this is a previous IIT question of complex numbers .I have put the question in the attachment Can you help me solve it? The answer given is A,B,C
4 years ago

Answers : (1)

mycroft holmes
272 Points 
							
$Re (z_1 \overline{z_2})=0 \Rightarrow z_1, z_2 are perpendicular
 
i.e. z_1 = (\cos \theta, \sin \theta); z_2 = (-\sin \theta, \cos \theta) for some angle 
 
Then w_1 = (\cos \theta, -\sin \theta); w_2 = (\sin \theta, \cos \theta)
 
Then its immediately seen that |w_1| = 1 ,|w_2| = 1 and w1 and w2 are also perpendicular. Which means that Re (w_1 \overline{w_2})= 0
 
4 years ago
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