Let be a real number, then is a point on the unit-circle (radius 1, center at 0) in the complex plane, where is the angle in radians corresponding to that point as seen from the origin 0, and relative to the positive direction of the real axis.

Because of this, the real part of that complex number is , and its imaginary part is .

Overall, you get the relationship .

(See also: Euler's formula - Wikipedia, the free encyclopedia).

What you get, therefore, is in the case of

and in the case of .