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← IIT-JEE 2008 · Paper 2
MathematicsSingle correct+3 / -1Question 1 of 66

IIT-JEE 2008 · Paper 2, Mathematics question 1

A particle PP starts from the point z0=1+2iz_0=1+2i, where i=−1i=\sqrt{-1}. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1z_1. From z1z_1 the particle moves 2\sqrt2 units in the direction of the vector i^+j^\hat i+\hat j and then it moves through an angle π2\frac\pi2 in anticlockwise direction on a circle with centre at origin, to reach a point z2z_2. The point z2z_2 is given by

Choose one option
Answer and worked solution

Official answer: D

Moves.

  • 5 units horizontally away from the origin: 1+2i→6+2i1+2i\to6+2i.
  • 3 units vertically away: 6+5i=z16+5i=z_1.
  • 2\sqrt2 units along i^+j^\hat i+\hat j: 7+6i7+6i.
  • A quarter turn anticlockwise about the origin multiplies by ii: i(7+6i)=−6+7ii(7+6i)=-6+7i.

(D) z2=−6+7iz_2=-6+7i

Topics:Geometry in the complex plane
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