How do you find the square root of 8i?
#8i = 8(cos (pi/2) + i sin (pi/2))#
Hence by de Moivre's theorem, one square root is:
#sqrt(8)(cos(pi/4)+isin(pi/4)) = 2sqrt(2)(1/sqrt(2)+1/sqrt(2)i) = 2+2i#
This is the principal square root. The other square root is