Not quite as simple as that.

*i* is imaginary, but the number space occupied by real and imaginary numbers can be thought of as a circle (or at least as a 2 dimensional plane in which a circle can be drawn through the points *1*, *1i*, *-1*, and *-1i*).

If one draws a line, where positive real numbers are to the right, and negative real numbers are to the left; then one can draw a perpendicular line, where negative imaginary numbers are down, and positive imaginary numbers are up.

You can then draw a line where *X*^{2} + iY^{2} = 1, and this line will be a circle through the points where *X = 1* and *Y = 0*, *X = 0* and *Y = 1*, *X = -1* and *Y = 0*, and *X = 0* and *Y = -1*.

The *e*^{iπ} = -1 is based on the more general formula that *e*^{iθ} = cos(θ) + i sin(θ), and since *cos(π) = -1* and *sin(π) = 0*, so *cos(π) + i sin(π) = -1 + 0 i = -1*.