A complex exponential of unit magnitude traces the unit circle. Its real and imaginary parts are the horizontal and vertical projections, so multiplication by represents a rotation.模长为一的复指数沿单位圆运动。实部和虚部分别是水平、竖直投影，因此乘以 对应一次旋转。
The rotating radius and its projections share one angle. The curve on the right records the imaginary part, , as that angle increases.旋转半径与两个投影共用同一个角度。右侧曲线记录角度增大时的虚部 。