A man walks a distance of 3 units from the origin towards the North-East (N 45^ E) direction. From there, he walks a distance of 4 units towards the North-West ( N 45^ W ) direction to reach a point P . Then, the

Correct answer: D. (3+4 i) e^ i π / 4 Let O A=3 , so that the complex number associated with A is 3 e^ i π / 4 . If z is the complex number associated with P , then array rlrl & & z-3 e^ i π / 4 0-3 e^ i π / 4 & =(4)/(3)e^ -i π/ 2 =-(4 i)/(3) & 3 z-9 e^ i π/ 4 & =12 i^ i π/ 4 & z & z & =(3+4 i) e^ i π/ 4 array

JEE Advanced 2007Paper 1

Exam: JEE Advanced
Year: 2007
Paper: Paper 1
Subject: Mathematics
Chapter: Complex Number

JEE Advanced 2007 · Paper 1 · Mathematics · Complex Number

A man walks a distance of 3 units from the origin towards the...

A man walks a distance of 3 units from the origin towards the North-East

\left(\mathrm{N} 45^{\circ} \mathrm{E}\right)

direction. From there, he walks a distance of 4 units towards the North-West (

\mathrm{N} 45^{\circ} \mathrm{W}

) direction to reach a point

P

. Then, the position of

P

in the Argand plane is A man walks a distance of 3 units from the origin towards the North-East (N 45^ E) direction. From there, he walks a

Options

A $3 e^{i \pi / 4}+4 i$
B $(3-4 i) e^{i \pi / 4}$
C $(4+3 i) e^{i \pi / 4}$
D $(3+4 i) e^{i \pi / 4}$

Correct answer

D. $(3+4 i) e^{i \pi / 4}$

Step-by-step solution

Let

O A=3

, so that the complex number associated with

A

3 e^{i \pi / 4}

. If

z is the complex number associated with

, then

\begin{array}{rlrl}& & \frac{z-3 e^{i \pi / 4}}{0-3 e^{i \pi / 4}}& =\frac{4}{3}e^{-i \pi/ 2}=-\frac{4 i}{3}\\ \Rightarrow & 3 z-9 e^{i \pi/ 4} & =12 i^{i \pi/ 4} \\ \Rightarrow & z & z & =(3+4 i) e^{i \pi/ 4} \end{array}

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