Complex NumbersHard
Question
If z, z1 and z2 are complex numbers such that z = z1.z2 and |
- z1 ≤ 1. then maximum value of |z| - Re(z) is -
- z1 ≤ 1. then maximum value of |z| - Re(z) is -Options
A.0
B.2
C.
D.
Solution
|
- z1|2 = |z2|2 + |z1|2 - 2Re(z1z2)
= (|z2| - |z1|)2 + 2(|z| - Re (z))
∴ |z| - Re(z) =
∴ |z| - Re(z) <
- z1|2 = |z2|2 + |z1|2 - 2Re(z1z2)= (|z2| - |z1|)2 + 2(|z| - Re (z))
∴ |z| - Re(z) =
∴ |z| - Re(z) <
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