Prove that u(x) : = e* (x cos y – ysiny) is harmonic and find a conjugate function of u.

Step-by-step explanation:

As given in question,

For a system to be harmonic,

From the above calculated value we can see that

= 0

So, given function u(x) is harmonic.

Now to find conjugate function of u,

According to Cauchy-Riemen Equation,

So, we4 can write the above equation as,

on  putting the values, we have

on integrating both side, we get

hence, the conjugate equation can be given by

idk

step-by-step explanation: