Circular motion can be described using complex numbers. Let the x axis be the real axis and the y axis be the imaginary axis. The position of the body can then be given as z , a complex "vector": z = x + i y = R ( cos ⁡ ⁡ [ θ θ ( t ) ] + i sin ⁡ ⁡ [ θ θ ( t ) ] ) = R e i θ θ ( t ) , where i is the imaginary unit, and θ θ ( t ) is the argument of the complex number as a function of time, t.