complex number問題

(a) z(1+i)^4=(a+3i)^2
|z(1+i)^4|=|(a+3i)^2|
Since |(1+i)|=√2
We have 3*4=a^2+9=>a=-√3

(b) (1+I)^4=4[cosπ+isinπ]=-4
(-√3+3i)^2=12[cos5π/3+isin5π/3]
So z=-3[cos5π/3+isin5π/3] which shows that the required smallest number is n=3