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ANSWER
[tex]2(\cos 30+i\sin 30)[/tex]EXPLANATION
We want to convert the complex number to polar form:
[tex]\sqrt[]{3}+i[/tex]The general polar form of a complex number is:
[tex]r(\cos \theta+i\sin \theta)[/tex]where:
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \theta=\tan ^{-1}(\frac{y}{x}) \end{gathered}[/tex]Note: x is the real part of the complex number while y is the coefficient of i.
Therefore, from the number given:
[tex]\begin{gathered} x=\sqrt[]{3} \\ y=1 \end{gathered}[/tex]We now have to find r and θ:
[tex]\begin{gathered} \Rightarrow r=\sqrt[]{(\sqrt[]{3})^2+1^2}=\sqrt[]{3+1} \\ r=\sqrt[]{4} \\ r=2 \\ \Rightarrow\theta=\tan ^{-1}(\frac{1}{\sqrt[]{3}}) \\ \theta=30\degree \end{gathered}[/tex]Therefore, the polar form of the complex number is:
[tex]\begin{gathered} 2\cos 30+2i\sin 30 \\ \Rightarrow2(\cos 30+i\sin 30) \end{gathered}[/tex]
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