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Let O be the origitn and point A be repr...

Let O be the origitn and point A be represented by z. If OA is rotated throught an angle `po//2` in the anticlockwise direction keeping the length of OA same, then what represents the new point ?

A

`-iz`

B

`|z|i`

C

`iz`

D

z

Text Solution

Verified by Experts

The correct Answer is:
C
Let `z=cos theta+I sin theta`
Now, on rotaing through and angle `(pi)/(2),z` bcomes `Z=cos""((pi)/(2)+theta)+sin""((pi)/(2)+theta)`
`=-sin theta+icos theta=i^(2)sin theta+icos theta`
`= i (cos theta +isin theta)=iz`
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