How to plot imaginary (or real) part of one complex variable vs another real variable of an implicit function in MATLAB? For example,

[Torsten]

Hint:

Given t as a real number, do you know the solution(s) for z giving z^2+t^2+1=0 ?

[Walter Roberson]

Re(z) has no particular relationship to t so graph anything you want.

The statement that "f(z,t)=0 doesn't have any real solutions" is irrelevant to the question.

Answer 1

[Gyan Vaibhav]

Hi Kartik,

I understand that you are trying to plot the real and imaginary parts, for the cases in which “t” is a real value in the above implicit function.

The plots for the imaginary and real parts for the complex values of z for the implicit function can be plotted as follows:

1. Define the implicit function. In this case, the function is
2. Since it is required to plot and , the z term can be isolated as follows to express the function as .
3. Choose a range of t values for which it is required to generate the plot. For instance, t can be defined as t = -2:0.1:2 to create a vector of values from -2 to 2 with increments of 0.1.
4. Calculate the real and imaginary parts of z for each t value. For this MATLAB's built-in “real” and “imag” functions can be used to extract the real and imaginary parts, respectively.
5. Plot the real and imaginary against t values.

However, the following points need to be kept in mind.

1. Note that the “sqrt” function in MATLAB returns the principal square root, which is always non-negative. Since the imaginary part can be positive or negative, it might be required to plot both positive and negative values to represent both possible values of the imaginary part of “z”.
2. Since “z” is purely imaginary in this case, so the real part of “z” will always be zero.

Consider the following pages to learn more about extracting the real and imaginary parts of a complex number.

• Real part of complex number: https://www.mathworks.com/help/matlab/ref/real.html
• Imaginary part of complex number: https://www.mathworks.com/help/matlab/ref/imag.html

Hope this helps.

Thanks

Gyan

[Dyuman Joshi]

@Gyan Vaibhav, Please don't do obvious homework questions on Answers, when no effort has been shown. This does not help the student, who learns nothing more than to post all of their homwork problems on the site, hoping they will find someone willing to do their thinking and work for them. Worse that that, it convinces the next student who comes along to do the same.

If you want to help, then find a way to push the student in the right direction. Just as Torsten has done above. But posting a complete solution does far more harm than good.

[Gyan Vaibhav]

Hi Dyuman,

Thank you for guiding me in that direction. I will keep this in mind from now on. Or if you suggest I can omit the code.

[Dyuman Joshi]

@Gyan Vaibhav Yes, you should omit the code.