TiNspire : Complex Analytic and Harmonic Functions

In Complex Analysis you will be asked to check if a complex function is analytic which requires checking the 2 Cauchy Riemann Conditions. Fortunately, the TiNspire has the ability to deal with those and we can go ahead and solve those problems using the Complex Analysis Made Easy app at www.TinspireApps.com to solve those problems step by step.

Say we are given a complex valued function in the format u+i*v such as x^2-y^2+i*2*x*y as shown below. Out comes the solution with steps showing that this function is indeed analytic. Insiders realize that this is actually the function f(z)=z^2

When entering z^2 in the top box we will get naturally the same answer. See below

Next Question: Is a given Complex Function Harmonic? And if so what is its harmonic conjugate ?

Lets select that option in the menu as shown below:

Lets answer the first question first : Is e^(-3x)*cos(3y) harmonic ? Well, let’s just enter it as shown below:

Voila! It is Harmonic. And we understand why 😉

Lastly, let’s find the harmonic conjugate function to x^2-y^2 , entered as shown below:

Beautiful, good thing we have our handy dandy TiNspire to provide those answers.