How do you find the nth root of -1?

1 Answer
Shwetank Mauria
Oct 21, 2016

#n^(th)# root of #-1# is #cos(pi/n)+isin(pi/n)#

Explanation:

According to De Moivre's theorem, if a complex number #z# in polar form is given by

#z=r(costheta+isintheta)#, then

#z^n=r^n(cosntheta+isinntheta)#

Let #z^n=-1=1(cospi+isinpi)# as #cospi=-1# and #sinpi=0#

Hence #z# the #n^(th)# root of #-1# will be

#cos(pi/n)+isin(pi/n)#

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