JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Complex Numbers

z

and

w

are two complex numbers such that

∣ z w ∣ = 1

and

ar g (z) - ar g (w) = \frac{π}{2}

, then

Answer: (D)

Solution

Write

z

and

w

in polar form with

∣ z ∣∣ w ∣ = 1

and the argument of

z

exceeding that of

w

\frac{π}{2}

. Then

\overset{z}{ˉ} w

has modulus

∣ z ∣∣ w ∣ = 1

and argument

- ar g z + ar g w = - \frac{π}{2}

, so

\overset{z}{ˉ} w = e^{- iπ /2} = - i

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option