Answer
\[\cos 2x+i\sin 2x\]
Where $u(x)=\cos 2x$ and $v(x)=\sin 2x$
Work Step by Step
We will use euler's formula
\[e^{i\theta}=\cos \theta+i\sin \theta\]
We can write
$e^{2ix}=e^{i(2x)}$
By Using euler's formula
$e^{2ix}=\cos 2x+i\sin 2x$
Here $u(x)=\cos 2x$ and $v(x)=\sin 2x$.
Hence $e^{2ix}=\cos 2x+i\sin 2x$.
