Question 454435
Perhaps use Euler's formula, which says that


*[tex \LARGE e^{i\alpha} = \cos(\alpha) + i\sin(\alpha)]


Suppose we want to divide two arbitrary complex numbers (a+bi)/(c+di). If we suppose


*[tex \LARGE a+bi = \sqrt{a^2 + b^2}e^{i\alpha}]
*[tex \LARGE c+di = \sqrt{c^2 + d^2}e^{i\beta}] (alpha, beta are the arguments of the complex numbers)


Then,


*[tex \LARGE \frac{a+bi}{c+di} = \frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}} \frac{e^{i\alpha}}{e^{i\beta}} = \frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}}e^{i(\alpha - \beta)} = \frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}} (\cos(\alpha - \beta) + i\sin(\alpha - \beta))]


Graphing this number isn't too difficult. Here, we locate the complex number with argument alpha - beta and magnitude 1, then scale it by that coefficient on the left. That is the quotient of the two complex numbers.