Pie?

Cool!!

I don't think so....unless you use the imaginary plane which would be too complicated.

Is there any kind of graphical representation of the world-famous formula of e^pi i equals to -1?

$e^{i\theta}=cos\theta+isin\theta$

sometimes it is called   $cis\theta$

so  

Here is a general picture (not for pi radians  BUT the angle must be measured int radians)

This is referred to as the unit circle on a complex grid..  The centre is (0,0)  and the radius is  1 unit.

The horizontal unit is real

and the vertical unit is imaginary

so if theta = pi radians     

Look here if you would like to work through a little more cool mathemathics :)

https://www.mathsisfun.com/algebra/complex-number-multiply.html

This animated graphic is my favorite.

This gives an idea of the light and shadow and the knowledge and imagination of the science and mathematics that is Euler.

Ah ha I found the site I was looking for!!

https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html

The height which is red is the sine value - it is also the y value on the unit circle

This is becasue 

$sin\theta =\frac{opp}{hyp}=\frac{y}{1}=y$

The horizontal distance is cosine theta - it is the x valuc of any point on the unit circle

Because

$cos\theta = \frac{adj}{hyp}=\frac{x}{1}=x$

So any (x,y) point on this unit circle is given by   $(cos\theta,\;sin\theta)$