How do you write the complex number in trigonometric form #-2(1+sqrt3i)#?

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Answer 1 · 2017-02-23T07:58:21

The trigonometric form is #=-4(cos(pi/3)+isin(pi/3))#

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

#z=r(costheta+isintheta)#

Here, we have

#z=-2(1+sqrt3i)#

The modulus is

#|z|=-2sqrt(1+3)=-2*2#

#z=-4(1/2+sqrt3/2i)#

#costheta=1/2# and #sintheta=sqrt3/2#

#theta=pi/3#

Therefore,

#z=-4(cos(pi/3)+isin(pi/3))#

#=-4e^(pi/3i)#