Polar and exponential forms of complex numbers

Polar multiplication and real powers

[Maximum mark: 8]Consider the complex numbers $z_1=\sqrt3+i$,
$z_2=1+i$ and $w=z_1\cdot z_2$(a) By expressing $z_1$ and $z_2$ in modulus-argument
form, write down(i) the modulus of $w$(ii) the argument of $w$[6](b) Find the smallest positive integer value of $n$,
such that $w^n$ is a real number[2]