Find the modulus and argument of the complex number (1 + 2i)/(1 - 3i)

Question

Find the modulus and argument of the complex number \(\frac{1+2i}{1-3i}\)

(1 + 2i)/(1 - 3i)

Answer 1

Let z = \(\frac{1+2i}{1-3i}\) 

This is of the form a + bi, where a = -1/2, b = 1/2

\(\therefore\) modulus = r

If θ  is the argument, then

Hence, modulus = \(\frac{1}{\sqrt2}\) and argument = \(\frac{3\pi}4\)