Question

The point represented by the complex number 2-i

Answer 1

Answer:

..................(2,-1)

Answer 2

Given Question :

The point represented by the complex number 2 - i is rotated about origin through an angle $\frac{\pi}{2}$ in the clockwise direction, the new position of point is ?

To find : The new position of point

Given : 2 - i

Here,            Z = 2 - i              $\theta$ = - $\frac{\pi}{2}$    

                    $Z^{\prime}=Z \cdot e^{+i \theta}$                                          

             $Z^{\prime}=Z \cdot(\cos \theta+i \sin \theta)$   ---> ( Where, $e^{+i \theta}$  )

Applying "Z" and "$\theta$" values, in we get

             $Z^{\prime}=Z \cdot(\cos \theta+i \sin \theta)$

             $Z^{\prime}=( 2 - i) \cdot(\cos (-\frac{\pi }{2}) +i \sin (-\frac{\pi }{2}) )$

Hence, the value of   $cos (-\frac{\pi }{2} )$ = 0  ;   $sin (-\frac{\pi }{2} )$ = -1  

             $Z^{\prime}=( 2 - i) \cdot(0 +i \ (-1) )$

             $Z^{\prime}=( 2 - i) \cdoti \ (-i)$

             $Z' = (-2i - i^{2} )$

             $Z' = (-2i - (-1) )$ ---> ( $i^2$ = -1 )

             $Z' = (-2i +1 )$

             $Z' = - (2i - 1 )$ = - 1 -2i.

             $Z' = -1 - 2i$.        

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