How do you find the square root of 8i?

2 Answers
Mar 25, 2018

Answer:

#2sqrt(2i)#

Explanation:

#sqrt(8i)#

#sqrt(4*2*i) rarr# 4 is a perfect square; it can be taken out of the radical

#2sqrt(2i)#

Mar 25, 2018

Answer:

#sqrt(8i) = 2+2i#

Explanation:

Note that:

#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 #-2-2i#