Complex NumbersHard

Question

Let z1 and z2 be complex numbers such that z1 ≠ z2 and |z1| = |z2| If z1 has positive real part and z2 has negative imaginary part, then may be

Options

A.zero
B.real and positive
C.real and nergative
D.purely imaginary

Solution

Given, |z1|= |z2|
Now,    
       
       
                (∵ |z1|2 = |z2|2)
As, we know z - = 2i Im (z)
∴         z21 - z12 = 2i Im (z21)
∴        
Which is purely imaginary or zero.
Therefore, (a) and (b) are correct answers.

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