question_answer

The point represented by 2+i in the Arg and plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 2 units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :   JEE Main Online Paper (Held On 09 April 2016)

A) 2 + 2i                     

B) - 2 - 2i

C) 1 + i       

D) - 1 - i

Correct Answer: C

Solution :

Let P(2 + i) By rotation theorem \[\frac{z-(3+3i)}{3+i-(3+3i)}=\frac{2\sqrt{2}}{2}{{e}^{(-\pi /4)i}}\] \[\frac{z-3-3i}{-2i}=1-i\] \[z-3-3i=-2i-1\] \[z=1+i\]