Theorem 3.5 (Polar Form of the
Cauchy-Riemann
equations). Let
be
a continuous function that is defined in some neighborhood of the
point
. If
all the partial derivatives
are
continuous at the point
and if the polar form of the Cauchy-Riemann equations,
(3-22)
and
,
holds, then
is differentiable at
,
and we can compute the derivative
by using either
(3-23)
, or
(3-24) ![]()
.
Proof.
Proof of Theorem 3.5 is an exercise in the book.
Complex Analysis for Mathematics and Engineering