The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 2 units in the south-west wards direction. Then its new position in the Argand plane is at the

Correct answer: A. 1 + i Let P(2 + i) and S(z) By Rotation theorem, rotating about 3 + 3i , we get (z - (3 + 3i))/((3 + i) - (3 + 3i)) = 2 2 2 e ^ - (iπ)/(4) ⇒ (z - 3 - 3i)/(- 2i) = 1 - i ⇒ z - 3 - 3i = - 2i - 2 ⇒ z = 1 + i

JEE Main 20169 AprilOnline

Exam: JEE Main
Year: 2016
Date: 9 April
Mode: Online
Subject: Mathematics
Chapter: Complex Number

JEE Main 2016 · 9 April · Online · Mathematics · Complex Number

The point represented by 2 + i in the Argand plane moves 1 unit...

The point represented by

2 + i

in the Argand plane moves

1

unit eastwards, then

2

units northwards and finally from there

2\sqrt{2}

units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by : The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from

The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from

Options

A $1 + i$
B $2 + 2i$
C $- 2 - 2i$
D $- 1 - i$

Correct answer

A. $1 + i$

Step-by-step solution

The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from

Let $P\left(2 + i\right) \text{ and } S(z)$
By Rotation theorem, rotating about $3 + 3i$ , we get

$\dfrac{z - \left(3 + 3i\right)}{\left(3 + i\right) - \left(3 + 3i\right)} = \dfrac{2\sqrt{2}}{2}{e}^{- \dfrac{i\pi}{4}}$

$⇒ \dfrac{z - 3 - 3i}{- 2i} = 1 - i$

$⇒ z - 3 - 3i = - 2i - 2 ⇒ z = 1 + i$

Practice Complex Number on Quantrex Academy →

More from Complex Number