QJEEM21Ma96e2: JEE Main 2021 Mathematics - Class 11 JEEM21Ma96e2 Solution: Let a complex number be w = 1 i. Let another complex number z…

Question

Verified Solution • 2025–26 Session moderate

Let a complex number be w = 1

-

{\sqrt 3 }

i. Let another complex number z be such that |zw| = 1 and arg(z)

-

arg(w) =

{\pi \over 2}

. Then the area of the triangle with vertices origin, z and w is equal to :

Accepted Answer

Given, w = 1

-

\sqrt 3

i

\Rightarrow |w| = \sqrt {{{(1)}^2} + {{( - \sqrt 3 )}^2}} = 2

Also, given | zw | = 1

\Rightarrow

| z | | w | = 1 (using property)

\Rightarrow

| z | =

{1 \over 2}

Also, arg(z)

-

arg(w) =

{{\pi {} } \over 2}

\therefore

Angle between two complex number z and w is

{{\pi {} } \over 2}

.

\therefore

\angle zow = {{\pi {} } \over 2}

\therefore

\Delta

zow is a right angle triangle with base

ow = 2

and height

oz = {1 \over 2}

\therefore

Area =

{1 \over 2} \times 2 \times {1 \over 2} = {1 \over 2}

Step-by-Step Verified Solution