Complex NumbersHard
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
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