IIT-JEE 2007 · Paper 1 · Mathematics Q52

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MathematicsSingle correct+3 / -1Question 52 of 66

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

3e^{i\pi/4}+4i

(3-4i)e^{i\pi/4}

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

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

Answer and worked solution

Official answer: D

First leg. N 45° E is at 45° to the real axis: $3e^{i\pi/4}$ .

Second leg. N 45° W is at 135°, i.e. $4e^{i3\pi/4}=4i\,e^{i\pi/4}$ .

Sum. $P=3e^{i\pi/4}+4ie^{i\pi/4}=(3+4i)e^{i\pi/4}$ .

(D)

Topics:Polar and Euler form Geometry in the complex plane

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IIT-JEE 2007 · Paper 1, Mathematics question 52