Complex MATLAB

To begin the complex analysis version of FreeMat we were introduced to the fact that FreeMat has numerous predefined variables. We were asked to type in pi and the variables i and j into the command window.

For Exercise 1, we were then instructed to create some variables and to give them some complex number values. Then we were instructed to create variables D = (A*B)/C and E=(A+B)*C. Here is what we obtained:

Next we were introduced to four functions angle(Z), abs(Z), imag(Z), and real(Z) that would allow us to make conversions from rectangular to polar and vice versa.

For Exercise 1, we were asked to create variables A=3+4j, B=3-2j, and C=2<50 and to define and to compute D=(A+C)/B.  Here is what we obtained:

We then computed the angle in degrees and the magnitude of variable D. he is what we obtained:

For Assignment 1, we were to assign variables A1=3+2j, A2=-1+4j, and B=2-2j. First, we were to manually compute C=(A1*B)/A2 and then confirm this by using FreeMat. Here is what we obtained:

We were then to convert C into polar form.

We were now instructed to repeat the assignment for D=(A1+B)*A2.

Next we were given a system of two equations with complex numbers. Here is the process we used to solve this equation:

Next, we were shown how to find the roots of functions using the "roots" formula. More specifically, in Exercise 1 we were told to find the roots of x^2+4x+3. Here is what we obtained.

Now for  Assignment 2, we were instructed to find the roots of a few more functions x^2+x+4, x^3+3x^2+3, and x^4+3x^3+4x^2+2x+7. Here is what we obtained:

Lastly, we were asked to find the roots of the denominator of a Laplace Transform function s^3+5s^2+7s+3. Here is what we obtained:

To sum things up, I really enjoyed this lab assignment as much as I did with the first MATLAB assignment. I am now equipped with the tools needed to solve problems using complex numbers and variables.