1. If f(z) is analytic, then f'(z) exists.
(a) True   ; (b) False  .

2.  Function f(z) may be differentiable at z = z₀, but not analytic near z = z₀.
(a) True   ; (b) False  .

3.  Function v(x, y) = -3xy² + x³ is an harmonic function.
(a) True   ; (b) False  .

4.  The harmonic conjugate of u(x, y) = -2xy is
(a) x² + y² + c    ; (b) - x² - y² + c   ; (c) x² - y² + c    .

Notes