Express the comlex number (√3+i) in trigonometric form. Hence find the smallest positive integer n that (√3+i)^n is a real number.

This is how I have started it however im really not sure if this is right hoping someone could help.

ArgZ = tan^-1 (1/√3) = 30

|Z| = √3+1 = 2

Z = 2(cos30+isin30)

Is this correct??

Also how do i complete the question??

Thanks