$\phi(z) = Re(z) + f(z) $
where $f(z)$ is a meromorphic function. then WOTF is true,
1)$\phi $ is meromorphic
2)$\phi $ and $ f(z) $ has same number of singularities
3)$\phi $ is analytics in every closed and bounded region provided it has no poles
4)$\phi $ has no singularities
if i take $ f(z) =-z/2$ which is analytics and hence meromorphic then $Re(z) + f(z) = x + f(z)$ = $ (z+ \bar z)/2 -z/2 $ = $\bar z /2$ which is not analytics hence no point in talking about singularities. but none the option matches.