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