Put the following expressions into the shape $\displaystyle a+ib$ with $\displaystyle a,b \in \mathbb{R}$.

(a) $\displaystyle i^3$

(b) $\displaystyle (1-i)i$

The answers should be:

(a) $\displaystyle -i$

(b) $\displaystyle 1+i$

I know that the real and imaginary parts of a+ib are a and b respectively. But I don't know how to arrive at this answers, can anyone please explain? Thanks.