represent 1+2i/1-3iin the polar form

$z=\frac{1+2i}{1-3i}= \frac{1+2i}{1-3i}x\frac{1+3i}{1+3i} = \frac{-5+5i}{10}= \frac{-1+i}{2}$$$$\mathrm{If} z = x+\mathrm{iy} \mathrm{then} \left|Z\right|= \sqrt{x^2+y^2 } \mathrm{and} \mathrm{tan\theta }=\frac{y}{x}$$\left|z\right|=\sqrt{{\left(\frac{-1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2}=\frac{1}{\sqrt{2}} \mathrm{and} \mathrm{tan\theta }=\frac{1/2}{-1/2}=-1$$\mathrm{If} \mathrm{tan\theta } =1 \mathrm{then} \theta = \frac{\pi }{4}$$\mathrm{As} \mathrm{the} \mathrm{point} \left(-1/2, 1/2\right) \mathrm{is} \mathrm{in} \mathrm{second} \mathrm{quadrant}, \theta = \pi -\frac{\pi }{4}= \frac{3\pi }{4}$$\mathrm{Polar} \mathrm{form} \mathrm{of} z \mathrm{is} \frac{1}{\sqrt{2}}\left(\cos \frac{3\pi }{4} +i \sin \frac{3\pi }{4}\right)$">