The equation \log(z) = \log(r) + i\theta represents the logarithm of a complex number z . Here, r is the magnitude (or modulus) of z , and \theta is the argument (or angle) of z in the complex plane. This relationship shows how complex numbers can be expressed in terms of their polar coordinates. In this context, \log(r) gives the logarithm of the magnitude, while i\theta incorporates the imaginary unit i to account for the angle. This formulation is essential in fields like complex analysis and signal processing, where complex numbers are frequently used.