  A new simple geometrical interpretation of complex numbers is presented. It
differs from their usual interpretation as points in the complex plane. From
the new point of view the complex numbers are rather operations on vectors than
points. Moreover, in this approach the real, imaginary and complex numbers have
similar interpretation. They are simply some operations on vectors. The
presented interpretation is simpler, more natural, and better adjusted to
possible applications in geometry and physics than the usual one, especially
for describing rotations in a plane. The relation of the new approach to the
usual interpretation and especially to the notion of complex plane is also
clarified in the paper. The new interpretation of complex numbers gives new
insight into their applications in physics, which is demonstrated by some
elementary examples in mechanics and optics
