SATHEE: Complex Numbers 4 Question 3

Complex Numbers 4 Question 3

3.

A man walks a distance of 3 units from the origin towards the North-East ( $N 45^{\circ} E)$ direction. From there, he walks a distance of 4 units towards the North-West $(N 45^{\circ} W)$ direction to reach a point $P$ . Then, the position of $P$ in the Argand plane is

(2007, 3M)

(a) $3 e^{i π / 4} + 4 i$

(b) $(3 - 4 i) e^{i π / 4}$

(d) $(3 + 4 i) e^{i π / 4}$

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Answer:

Correct Answer: 3. (d)

Solution:

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

$\frac{z - 3 e^{i π / 4}}{0 - 3 e^{i π / 4}} = \frac{4}{3} e^{- i π / 2} = - \frac{4 i}{3}$

$\Rightarrow 3 z - 9 e^{i π / 4} = 12 i e^{i π / 4}$

$\Rightarrow \quad z =(3+4 i) e^{i \pi / 4}

Complex Numbers 4 Question 3

3.

Answer:

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Complex Numbers 4 Question 3

3.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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