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JEE Advanced2007MathematicsComplex NumberActual

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

Options

  1. A3 e^ i / 4 +4 i
  2. B(3-4 i) e^ i / 4
  3. C(4+3 i) e^ i / 4
  4. D(3+4 i) e^ i / 4

Correct answer

D. (3+4 i) e^ i / 4

Step-by-step solution

Let O A=3 , so that the complex number associated with A is 3 e^ i / 4 . If z is the complex number associated with P , then array rlrl & & z-3 e^ i / 4 0-3 e^ i / 4 & = 4 3 e^ -i / 2 =- 4 i 3 & 3 z-9 e^ i / 4 & =12 i^ i / 4 & z & z & =(3+4 i) e^ i / 4 array

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