Answer:
See explanation
Step-by-step explanation:
The given complex number are:
[tex]z_1=-3\sqrt{3}+3i[/tex]
and
[tex]z_2=6\cos 150\degree+6i\sin 150\degree[/tex]
When we rewrite [tex]z_1=-3\sqrt{3}+3i[/tex] in complex form, we obtain;
[tex]z_1=r(\cos \theta+i\sin \theta)[/tex]
where
[tex]r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6[/tex]
and
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]
[tex]\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree[/tex]
Hence,
[tex]z_1=6(\cos 150\degree+i\sin 150\degree)[/tex]
[tex]z_1=6\cos 150\degree+6i\sin 150\degree[/tex]
Hence
[tex]z_1=z_2[/tex]
