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,

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

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

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