Complex Variables and Partial Differential Equations (3130005)

Analytic functions

BE | Semester3 Topic : Analytic functions

Q3 (b) Winter-2019
Check whether the following functions are analytic or not at any point,

$f (z) = 3 x + y + i (3 y - x)$

$f (z) = z^{\frac{3}{2}}$

4 Marks

Unit : Complex variable functions

Q3 (b) Winter-2019
If $f (z) = u + iv$ , is an analytic function,prove that $(\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}}) {|Re f (z)|}^{2} = 2 {|f^{'} (z)|}^{2}$ .

4 Marks

Unit : Complex variable functions