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  • The point represented by the complex number 2 – i is rotated about origin through an angle π/2 in the clockwise direction, the new position of point is: A. 1 + 2i B. –1 – 2i C. 2 + i D. –1 + 2i

The point represented by the complex number 2 -i is rotated about origin through an angle \pi/2 in the clockwise direction, the new position of point is:
A. 1 + 2i
B. -1-2i
C. 2 + i
D. -1 + 2i

Answers (1)

The answer is the option (b).

If z rotated through an angle of \pi/2 about the origin in clockwise direction .

Then the new position =z.e^{-\left ( \frac{\pi}{2} \right )}

=\left (2-i \right ).e^{-\left ( \frac{\pi}{2} \right )}

=\left (2-i \right ).\left [ \cos\left (- \frac{\pi}{2} \right )+isin\left (- \frac{\pi}{2} \right ) \right ]

=\left (2-i \right ).\left (0-i \right )

=-1-2i

Hence, the correct option is (b)

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