Complex $2$ to the exponential form

Question

I am trying to find the exponential form of the complex number $2$. There is no imaginary part given, just the real part $2$. Because of this I'm sort of confused how to treat this as a 'complex number'. What value does the imaginary part have?

The solution is supposed to be $2e^{2k\pi j}$.

Any help would be greatly appreciated.

Answer 1

$$r=|2+0i|=2$$

$$\theta=\arctan(\underbrace{0/2}_{\text{imaginary/real}})+2\pi k=2\pi k$$

Thus,

$$2=re^{j\theta}=2e^{2\pi kj}$$