Let f(z) = (z3 + 1) sin z2 for z ∈ ℂ. Let f(z) = u(x, y) + iv (x, y),
where z = x + iy and u, v are real-valued functions. Then which of the following are true?
1
u : ℝ2 → ℝ is infinitely differentiable
2
u is continuous but need not be differentiable
3
u is bounded
4
f can be represented by an absolutely convergent power series \(\sum_{n=0}^{\infty} a_n z^n\) for all z ∈ ℂ