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The point represented by the complex num...

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

A

`1 +2i`

B

`- 1- 2i`

C

`2 + i`

D

`- 1 + 2i`

Text Solution

Verified by Experts

The correct Answer is:
B
Givne that, `z = 2 - i`
It is rotated about origin through an angle `(pi)/(2)` in the clockwise direction
`:. "Now Position" = ze^(-ipi//2) = (2 - i )e^(-ipi//2)`
`=(2 -i)["cos"((-pi)/(2))+ isin((-pi)/(2))] = (2 -i) [0 -i]`
`= - 2i - 1 = -1 - 2i` .
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