Walking in Argand Plane (JEE Problem)

Algebra Level 4

A man walks a distance of 3 units from the origin towards the North - East (N 4 5 45^{\circ} E) direction.From there,he walks a distance of 4 units towards North - West (N 4 5 45^{\circ} W) direction to reach a point P \color{#3D99F6}P .
Then, position of point P \color{#3D99F6}{P} in the argand plane is:

Details :

  • i = 1 i = \sqrt{-1}
4 e i π 4 + 3 i 4e^{\frac{i\pi}{4}} + 3i 3 e i π 4 + 4 i 3e^{\frac{i\pi}{4}} + 4i ( 3 + 4 i ) e i π 4 ( 3 + 4i ) e^{\frac{i\pi}{4}} ( 4 + 3 i ) e i π 4 ( 4 + 3i ) e^{\frac{i\pi}{4}} ( 4 3 i ) e i π 4 ( 4 - 3i ) e^{\frac{i\pi}{4}} ( 3 4 i ) e i π 4 ( 3 - 4i) e^{\frac{i\pi}{4}} 3 e i π 4 4 i 3e^{\frac{i\pi}{4}} - 4i

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