A particle P starts from the point z0=1+2i where i=√−1
| A particle P starts from the point z0=1+2i, where i=√−1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves √2 units in the direction of the vector ^i+^j and then it moves through an angle π2in anti-clockwise direction on a circle with centre at origin, to reach a point z2. The point z2 is given by
A. 6 + 7i
B. -7 + 6i
C. 7 + 6i
D. -6 + 7i
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
z′2=(6+√2cos45∘,√2sin45∘)=(7,6)=7+6i
By rotation about (0,0)
z2z′2=eiπ2
=(7+6i)(cosπ2+i sinπ2)=(7+6i)(i)=−6+7i
