The equation z = re^i\theta represents a complex number in polar form, where r is the magnitude (or modulus) and \theta is the angle (or argument) measured in radians. This form is useful because it simplifies multiplication and division of complex numbers, as well as finding roots. In this expression, e^i\theta is derived from Euler's formula, which states that e^i\theta = \cos(\theta) + i\sin(\theta) . Thus, the polar form can also be expressed as z = r(\cos(\theta) + i\sin(\theta)) , linking complex numbers to trigonometric functions.