find the modulus and arguments of the complex number $\displaystyle (1+\sqrt 3i)^3$.

my solution;

$\displaystyle (1+\sqrt 3i)(1+\sqrt 3i)(1+\sqrt 3i)$

$\displaystyle = 1+2\sqrt3i+3i^2(1+\sqrt 3i)$

$\displaystyle = -2+2\sqrt3i(1+\sqrt 3i)$

$\displaystyle = -2-2\sqrt3i+2\sqrt3i+2(3)i^2$

$\displaystyle = -2+6i^2$

$\displaystyle = -8$

is there anything wrong with my working above?

to find modulus and arguments of the complex number i need to express it in a+bi form first right? or can i assume b=0? being -8+0i

then |-8+0i| = 8

and arg |-8+0i| = 0