Question #c806f

1 Answer
Jan 9, 2018

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

Explanation:

The polar form #(r,theta)# of a complex number #(a,b)# is

#z=a+ib#

#z=r(costheta+isintheta)#

where

#r=||z||=sqrt(a^2+b^2)#

#costheta=a/(||z||)#

#sintheta=b/(||z||)#

Here,

#z=1-isqrt3#

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

Therefore,

#r=2#

#costheta=1/2#

#sintheta=-sqrt3/2#

#<=>#, #theta=-pi/3#