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Answer 1 · 2018-02-03T18:30:51

The polar form is #=2(cos(2/3pi)+isin(2/3pi))#

Let #z=-1+isqrt3#

#i^2=-1#

The polar form of a complex number #z=a+ib# is

#z=r(costheta+isintheta)#

The modulus is #r=|z|#

The argument is #=theta#

#costheta=a/(|z|)#

#sintheta=b/(|z|)#

Here,

#|z|=sqrt((-1)^2+(sqrt3)^2)=sqrt(1+3)=sqrt4=2#

#costheta=-1/2#

#sintheta=sqrt3/2#

Therefore,

The polar form is

#z=2(cos(2/3pi)+isin(2/3pi))=e^(i2/3pi)#