Plotting Complex Functions - Matlab for Non-Believers

Some equations, f(x), have complex roots that you can't see by just plotting using only real values of x. Here's how to plot complex roots of a function. Check out the rest of the PurdueMET channel at / purduemet . There is even a MATLAB playlist :-)

[@BennettAustin7]

“I dont know how to live in more dimensions, I’m an engineer not a physicist” haha

[@piyush9555]

😂, I'm sure physics will surely break this 3d barrier.

[@lammergeier100]

My hatred for MATLAB knows no bounds

[@purdueMET]

I understand. Matlab is handy, but it has it's quirks - the ancient user interface, for example. However, it's as close to a standard for technical computing as we have. I get a lot of students who have had terrible experiences learning Matlab. I wonder of part of the problem is that we're teaching it badly.

[@JonVlogs123]

@@purdueMET I think the problem has to do with lack of programming knowledge and/or practice. There is plenty of advice online so it is easy enough to self-teach.

[@NicolaeMPopa]

Excellent explanation, thank you so much!

[@abdurrehman6597]

this what ive been looking for, finally

[@chrisguitarvoyage]

in polar form: a = -2:0.1:1; b = -2:0.1:2; [A,B] = meshgrid(a,b); z = A+i*B; mag_z = abs(z); arg_z = angle(z); polar_z = mag_z.*exp(1i.*arg_z); y = 2*polar_z.^2 + 2*polar_z + 2; surfc(a,b,abs(y))

[@amaraamara-jq2xi]

thanks ...... excellence dear

[@abdurrahmantazkia5280]

thank you youtube for suggesting this video

[@Deepakfly]

The moment when he said “I don't know how to live in more dimensions, I’m an engineer not a physicist”. Congratulation for Scientist. Engineers made because of Physicist and Scientist.

[@purdueMET]

Thanks. We're all in this together and we need to support one another :-)

[@nestoraponte6674]

Me gustó el saludo jajaj, hola profe

[@sahibabd4741]

thank you very much. You helped me with this video. I wish you more excellence and brilliance

[@daoudandiaye3984]

Awesome. This gonna help me definitely dive into 4 d Space. Big thanks

[@amaraamara-jq2xi]

thank you very much

[@hyperdimensionallight4931]

This is great! Thank you :) So, the original Parabola is the slice through the surface where the imaginary part equals zero?

[@arts5852]

Very good and useful video. 👍 It also would be great to see, how we can do conformal mapping in MATLAB. P.s contour lines on this figure are Cassini ovals, aren’t they ?

[@WeAreGodsInFormation]

Can you make a video usings MatLab to sort, search or reorder arrays of data? Programing?

[@pabloj.g.g.471]

muchachos y muchachas !!!!!!!!

[@EaglesnAngels]

This is so incredible! Thank you very much for sharing this amazing content :D

[@yushengtzou]

Very very helpful~ Thank you sir!!!

[@henriqueleao4371]

What do i do if my function has more than one variable? f = (x^2 - 2*cos(z)*x*y + y^2)^(1/2)

[@emilioalbar.7624]

Did you find out how?

[@aashishpokhrel3854]

@@emilioalbar.7624 Did you find out?

[@IntegralMoon]

Its not true that real and imaginary are the only kinds of numbers. There are _many_ others. The dual numbers, the split-dual numbers, the quaternions. They aren't required to "close" our number system, but they definitely have their applications. For example, automatic differentiation (which matlab uses extensively) relies on the dual numbers.

[@purdueMET]

In the sense we normally think of numbers (associative, distributive and commutative properties), it's fair to limit the discussion to real and imaginary. Yes, there are certainly other entities, like quaternions, but they don't always obey the three properties we learned in school.

[@IntegralMoon]

Yep, thats true: not all of them do.

[@juancamilo1370]

Gracias profe!

[@nwxxzchen3105]

Can you map the complex number phase to the surface point color?

[@poincareelcartografo5406]

But shouldn't the surface be a hyperbolic paraboloid? Is there no way to represent it without using the absolute value? When I try to do it, Matlab gives me an error

[@purdueMET]

The surface is defined by a polynomial, so I don't think would be hyperbolic. I guess it depends on what you mean. To make the plot, I calculated a complex function value, F, and then plotted abs(F). If you are still stuck, send me an email ( [e-mail]) and I'll send you the code.

[@simeona.8058]

time 2:10 - 2:18

[@Sidnap882]

Gauss propoused that we should call positive real numbers - direct, negative real numbers - inverse, imaginary numbers - parralel. (Becouse of complex plane)

[@ncolyer]

ty

[@soumenmandal7212]

how to identify a real part in complex function in matlab?

[@purdueMET]

If you have a list of complex numbers, z, just type real(z)

[@jonejonson8832]

But...Z axis is Re() or Im() ?

[@gonzalezm244]

It's real, but not because it's the real part of the value of the function but because it is the modulus of that value, which is always real and positive. The modulus is also often written as |z|, r, sqrt(x^2+y^2), etc. It is the distance of the value of the function from the origin. Consequently, if the modulus of the function, |f(z)|, is zero, the value is 0 distance from the origin, so f(z) must also be zero. This is why we only need to look at the modulus to find the zeros of a complex function.

[@Pseudo___]

Let me introduce you to quaternions