GATE 2015 EE – SET 2 – Question1

Solution :

The sum of 2 differentiable function is always differentiable.

f(z) = g(z) + h (z)

g(z) = 4x + i5y ,h(z) = 5x + i4y  ,so

f(z) = (4x+i5y) + (5x + i 4y) = 9x + i9y = 9(x + iy) = 9z

Cauchy Riemann equataions
$$\frac{\partial u}{\partial x} $$=$$ \frac{\partial v}{\partial y}$$

$$\frac{\partial u}{\partial y} $$=$$ -\frac{\partial v}{\partial x}$$

f(z) is differentiable but g(z) and h(z) need not be differentiable at $$Z_{o}$$