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Question
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 ______.
Options
1 + 2i
–1 – 2i
2 + i
–1 + 2i
Solution
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 –1 – 2i.
Explanation:
Given that: z = 2 – i
If z rotated through an angle of `pi/2` about the origin in clockwise direction.
Then the new position = `z.e^(-(pi/2))`
= `(2 - i) e^(-(pi/2))`
= `(2 - i)[cos((-pi)/2) + i sin ((-pi)/2)]`
= (2 – i)(0 – i)
= –1 – 2i
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