Complex NumbersMedium
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) <
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
If | z − i| = 1 and amp(z) = π /2 (z ∈ 0), then z is-...If z (≠ - 1) is a complex number such that is purely imaginary, then |z| is equal to...If z = x + iy, then is equal to-...Let complex numbers α and lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2 respectively. I...The curve represented by z = , θ ∈ [0, 2π)...