Express z= -√3+ 3i in polar form ?

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Answer 1 · 2018-06-21T09:10:04

The polar form is #=2sqrt3(cos(2/3pi)+isin(2/3pi)#

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

#z=r(costheta+isintheta)#

where,

#{(x=rcostheta),(y=rsintheta),(tantheta=y/x),(r^2=x^2+y^2):}#

The complex number is #z=-sqrt3+3i#

#r=sqrt((-sqrt3)^2+(3)^2)=sqrt12=2sqrt3#

Therefore,

#z=2sqrt3(-sqrt3/(2sqrt3)+3/(2sqrt3)i)#

#z=2sqrt3(-1/2+sqrt3/2i)#

so,

#{(costheta=-1/2),(sintheta=sqrt3/2):}#

#theta# is in Quadrant #II#

#=>#, #theta=2/3pi#

Finally,

#z=2sqrt3(cos(2/3pi)+isin(2/3pi)#