= Solution
{c}
For the <continuously differentiable function> $f=u+iv$, the specified <Wirtinger derivative> is
$$
\frac{\partial f}{\partial\bar z}
=\frac12\bigl(u_x+iv_x+i(u_y+iv_y)\bigr)
=\frac12\bigl((u_x-v_y)+i(v_x+u_y)\bigr).
$$
A <complex number> vanishes exactly when both real and imaginary parts vanish. Consequently
$$
\boxed{\frac{\partial f}{\partial\bar z}=0
\iff u_x=v_y\text{ and }u_y=-v_x.}
$$
Thus the two real <Cauchy-Riemann equations> are one complex equation expressed by the <Wirtinger derivative>.
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