Find the modulus and argument of the complex number

Let us assume,

Now multiplying the numerator and denominator by 1 + 3i, we get:

=

=

=

=

Let us now assume,

∴

Now, by squaring the both sides we get:

As conventionally r > 0, thus

∴

Hence,

Thus, modulus of the given complex number =

And, argument of given complex number =