Find the modulus and argument of the following complex number and convert them in polar form: `(1+2i)/(1-3i)`

Explanation

Let `z=frac{1+2i}{1-3i}`

`z=frac{1+2i}{1-3i} xx frac{1+3i}{1+3i}`

`=frac{(1-6)+i(2+3)}{1+9}=-frac{1}{2}+frac{i}{2}`

`:. r=abs(z)=sqrt((-frac{1}{2})^2+(frac{1}{2}^2))=frac{1}{sqrt(2)}`

`tan alpha=abs(frac{-1/2}{1/2})=1`

`alpha=pi/4`

`theta=arg(z)=pi-alpha=3pi/4`

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