How do you find the square root of 5(cos120+isin120)?

1 Answer
Sep 13, 2016

+-sqrt 5/2(1+isqrt 3)

Explanation:

Use cos(180^o + a)=-cos a and sin (180^o + a)=-sin a

(5(cos 120^o + i sin 120^o))^(1/2)

sqrt 5(cos(2k(180)^o + 120^o)+i sin (2k(180)^o + 120^o))^(1/2

=sqrt 5(cos((2k(180) + 120^o)/2)+i sin(( (2k(180)^o + 120^o))/2)). k=0,1

=sqrt 5(cos 60^o + i sin 60^o)=sqrt 5/2(1+i sqrt 3), for k =0 and

=sqrt 5(cos 240^o + i sin 240^o), for k = 1

=sqrt 5(cos(180^o +60^o) + i sin(180^o + 60^o)

=-sqrt 5(cos 60^o + i sin 60^o)

=-sqrt 5/2(1+isqrt 3)