Complex NumbersMedium
Question
Let z & w are two complex numbers such that |z| = 1 & w = z + iz2. If z1 is value of z for which |w| is maximum, then sin
is equal to
is equal toOptions
A.
B.
C.
D.
Solution
|w| = |z + iz2| ≤ |z| + |iz2|
|w| is maximum when
z & iz2 having same argument
⇒ z = - i ⇒ amp(z) = -
sin
|w| is maximum when
z & iz2 having same argument
⇒ z = - i ⇒ amp(z) = -
sin
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
The centre of a square is at the origin and one of the vertex is 1 − i. The extremities of diagonal not passing th...If = 2 − z, then locus of z is a...In the region | z + 1 − i | ≤ 1 which of the following complex number has least positive argument -...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...If the complex numbers z1, z2, z3 represents vertices of an equilateral triangle such that | z1| = | z2 | = | z3 |, then...