Could someone, just check my answers, to see if I'm doing them right:

1) Find a real number $\displaystyle a$ such that:

$\displaystyle \mathbb{R}\left(\dfrac{1+2i}{a+3i}\right)=0$

Answer: $\displaystyle a=-6$

2) Factorise $\displaystyle x^6+1$ into real linear and quadratic factors.

$\displaystyle z^6+1=(z-1)(z+1)(z^2+z+1)(z^2-z+1)$

3) Find the real and imaginary parts of $\displaystyle (-1+i)^{77}$

Real part = $\displaystyle \dfrac{1}{\sqrt{2}}$

Imaginary part = $\displaystyle -\dfrac{1}{\sqrt{2}}$

Thanks