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) $(3 + 4 i) e^{i π / 4}$

(a) $3 e^{i π / 4} + 4 i$

(b) $(3 - 4 i) e^{i π / 4}$

(d)

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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

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

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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

Answer:

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Complex Numbers 4 Question 3

3. A man walks a distance of 3 units from the origin towards the North-East ( N45∘E) direction. From there, he walks a distance of 4 units towards the North-West (N45∘W) direction to reach a point P. Then, the position of P in the Argand plane is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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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