Is it true that for any complex function $f(z, t)$, the following equation is correct? $\frac{\partial f(z,t)}{\partial t} = \frac{\partial f^R(z,t)}{\partial t} + i \frac{\partial f^I(z,t)}{\partial t}$,
where $f(z,t) = f^R(z,t) + i f^I(z,t)$, z is complex number, t is real number(time), and $f(z,t)$ is complex number for all z and t.