Math, asked by 123arjunvmp9kq63, 1 year ago

if z= cos(π/3)-i sin (π/3) ,then z^2 -z+1 is equal to

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Answered by hukam0685
7

 z = \cos( \frac{\pi}{3} )  - i \sin( \frac{\pi}{3} )  \\ z =  (\frac{1}{2}  - i \frac{ \sqrt{3} }{2} ) \\ z =  \frac{1 - i \sqrt{3} }{2}
 {z}^{2}  =  \frac{1}{4}  \times (1 - 3 - i2 \sqrt{3} ) \\  =  \frac{1}{4} \times  - 2(1  +  i  \sqrt{3} ) \\  \frac{ - 1}{2} (1 + i \sqrt{3} )
now put the values in equation
 =  \frac{ - 1}{2} (1 + i \sqrt{3}) -  \frac{1}{2}  (1 - i  \sqrt{3} ) + 1
=
  = -  \frac{1}{2}  -  \frac{1}{2}  + 1 \\   = - 1 + 1 \\  = 0
option A. zero is the answer
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