Imaginary number in a graph

$\frac{i\sqrt{1}}{i\sqrt{3}}=\frac{1}{\sqrt{3}}$ which is a real number.

So, this number can be represented on a real number line. (No need for complex plane (argand diagram).)

Yes, we first "simplify" the number then we put it. 

And the number is not imaginary; it is real. 

That's very interesting! I know another strange fact that i^i is even real!

i = e^{pi/2i}

$e^{\pi i/2 \cdot e^{\pi i/2}}$ = $e^{\pi i^2 /2 }$

The i^2 cancels out as negative and we see that $e^{-\pi/2}$ = i ^i which is actually real!

Cool, isn't it! :)