How do i find P(2)? Let $P(x)$ be the polynomial of least degree with real coefficients such that $P(i)=P(1+i)=0$ and $P(1)=4$. Find $P(2)$.
Here i is the complex number. I have done such questions with real numbers but I don't know why I am not getting it.

Some hints:
1) When a polynomial has real coefficients the complex roots always come in conjugate pairs, i.e. if  $z = a+ib$ is a root, then $\overline{z} = a-ib$ is root as well.
2) A polynomial of degree $n$ can be written on the form
$$p(x)=\alpha\prod\limits_{k=1}^n(x-r_k) $$
where $r_k$ are the roots and $\alpha$ is the coefficient of the term with highest degree.
Example: A polynomial of degree 4 can be written as
$$p(x) = \alpha(x-r_1)(x-r_2)(x-r_3)(x-r_4) $$
