Complex coordinate
= Complex coordinate
{title2=$z=x+iy$}
Represent Cartesian coordinates $(x,y)$ in the plane by the <complex number> $z=x+iy$, whose <real part> and <imaginary part> recover them. Multiplication by $e^{i\theta}$ rotates the coordinates through angle $\theta$, so a rotating-frame calculation becomes a complex exponential change of variable.