Let a complex number be w = 1 - 3 i . Let another complex number z be such that | zw | = 1 and arg(z) - arg(w) = (π)/(2) . Then the area of the triangle (in sq. units) with vertices origin, z and w is equal to

Correct answer: B. (1)/(2) w = 1 - 3 i ⇒ | w | = 2 Now, |z| = (1)/(| w |) ⇒ |z| = (1)/(2) and amp (z) = (π)/(2) + amp (w) ⇒ Area of triangle = (1)/(2) . OP . OQ = (1)/(2) · 2 · (1)/(2) = (1)/(2) Sq. units

JEE Main 202118 MarchEvening Shift

Exam: JEE Main
Year: 2021
Date: 18 March
Shift: Evening Shift
Subject: Mathematics
Chapter: Complex Number

JEE Main 2021 · 18 March · Evening Shift · Mathematics · Complex Number

Let a complex number be w = 1 - 3 i . Let another complex number z...

Let a complex number be

w = 1 - \sqrt{3}i

. Let another complex number

z

be such that

| zw | = 1

and

arg\left(z\right) - arg\left(w\right) = \dfrac{\pi}{2}

. Then the area of the triangle (in sq. units) with vertices origin,

z

and

w

is equal to Let a complex number be w = 1 - 3 i . Let another complex number z be such that | zw | = 1 and arg(z) - arg(w) =

Options

A $4$
B $\dfrac{1}{2}$
C $\dfrac{1}{4}$
D $2$

Correct answer

B. $\dfrac{1}{2}$

Step-by-step solution

w = 1 - \sqrt{3}i ⇒ | w | = 2 $</p><p>Now, \left|z\right| = \dfrac{1}{| w |} ⇒ \left|z\right| = \dfrac{1}{2}$

and $amp \left(z\right) = \dfrac{\pi}{2} + amp \left(w\right)$

Let a complex number be w = 1 - 3 i . Let another complex number z be such that | zw | = 1 and arg(z) - arg(w) =

$⇒$ Area of triangle $= \dfrac{1}{2} . OP . OQ$

$= \dfrac{1}{2} \cdot 2 \cdot \dfrac{1}{2} = \dfrac{1}{2}$ Sq. units

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