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 position of P in the Argand plane is

Question

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 position of P in the Argand plane is [2007]

Smart Achievers · Accepted Answer

(4)

$\vec{O P} = \vec{O A} + \vec{A P}$

$\Rightarrow \vec{O P} = \vec{O A} + \vec{O B}$

$\Rightarrow \vec{O P} = 3 e^{i π / 4} + 4 e^{i (π / 2 + π / 4)}$

$= 3 e^{i π / 4} + 4 e^{i π / 2} e^{i π / 4}$

$= 3 e^{i π / 4} + 4 i e^{i π / 4}$

$= e^{i π / 4} (3 + 4 i)$

Solution

Q.
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 position of P in the Argand plane is [2007]

1 $3 e^{i π / 4} + 4 i$

2 $(3 - 4 i) e^{i π / 4}$

3 $(4 + 3 i) e^{i π / 4}$

4 $(3 + 4 i) e^{i π / 4}$

Ans.
(4)

$\vec{O P} = \vec{O A} + \vec{A P}$

$\Rightarrow \vec{O P} = \vec{O A} + \vec{O B}$

$\Rightarrow \vec{O P} = 3 e^{i π / 4} + 4 e^{i (π / 2 + π / 4)}$

$= 3 e^{i π / 4} + 4 e^{i π / 2} e^{i π / 4}$

$= 3 e^{i π / 4} + 4 i e^{i π / 4}$

$= e^{i π / 4} (3 + 4 i)$

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Solution

Q. 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 position of P in the Argand plane is [2007]

1 3eiπ/4+4i

2 (3-4i)eiπ/4

3 (4+3i)eiπ/4

4 (3+4i)eiπ/4

Ans. (4) OP→=OA→+AP→ ⇒OP→=OA→+OB→ ⇒OP→=3eiπ/4+4ei(π/2+π/4) =3eiπ/4+4eiπ/2 eiπ/4 =3eiπ/4+4i eiπ/4 =eiπ/4(3+4i)