Find all the complex roots Write the answer in the indicated

Find all the complex roots. Write the answer in the indicated from The complex squareroot s of 2 (cos 2 pi/3 + i sin 2 pi/3) Squareroot 2/2 + Squareroot 6/2 i, - Squareroot 2/2 - Squareroot 6/2 i Squareroot 2/2 - Squareroot 6/2 i, - Squareroot 2/2 + Squareroot 6/2 i

Solution

square root of 2 ( cos 2pi/3 + i sin 2pi/3 )

applying demoivres theorem

2 ( cos 2pi/3 + i sin 2pi/3 ) ^1/2

2^1/2 ( cos 2pi/3 + i sin 2pi/3 ) ^1/2

sqrt 2 ( cos pi/3 + i sin pi/3 )

+ - sqrt 2 ( 1/2 +i sqrt 3/2 )

+- (sqrt 2 / 2 + i sqrt 6/2 )

+ sqrt 2 / 2 + i sqrt 6/2 , - sqrt 2/2 - isqrt 6/2 ( option a )