Pick out the true statements:
(a) There exists an analytic function $f$ on $\mathbb{C}$ such that $f(2i) = 0$, $f(0) = 2i$ and $|f(z)|\le 2$ for all $z\in\mathbb{C}$
. (b) There exists an analytic function $f$ in the open unit disc $\{z\in\mathbb{C} : |z| < 1\}$ such that $f(1/2) = 1$ and $f(1/2^n ) = 0$ for all integers $n\ge 2 $.
(c) There exists an analytic function whose real part is given by $u(x, y) = x^2 + y^2$, where $z = x + iy$.