Thread: Plotting with complex numbers

Hi, I'm trying to plot a function like (2/3)Z + 1/(3Z^2), where Z is complex.

I understand the basic idea of Z^2 = (x+iy)*(x+iy)= x^2+ 2xyi - y^2 is represented as x^2 - y^2 in the real direction, and 2xy in the imaginary direction.

For the function I'm concerned with, however, there does not seem to be a way to break it into real and complex directions.

Please let me know if there needs to be further clarification.

Thank you!

Originally Posted by Aesun

Hi, I'm trying to plot a function like (2/3)Z + 1/(3Z^2), where Z is complex.

I understand the basic idea of Z^2 = (x+iy)*(x+iy)= x^2+ 2xyi - y^2 is represented as x^2 - y^2 in the real direction, and 2xy in the imaginary direction.

For the function I'm concerned with, however, there does not seem to be a way to break it into real and complex directions.

Please let me know if there needs to be further clarification.

Thank you!

Now split the right hand side into real and imaginary parts and plot.

CB

CaptainBlack, thank you for your help! Unfortunately I still don't see how to continue. Would you mind showing me a few more algebraic steps? I still can't seem to separate the real and imaginary parts.

Thank you!

Originally Posted by Aesun

CaptainBlack, thank you for your help! Unfortunately I still don't see how to continue. Would you mind showing me a few more algebraic steps? I still can't seem to separate the real and imaginary parts.

Thank you!

Put:



then:



and:



and:



Hence:



Now check the algebra for mistakes.

CB

Thank you so much! I'm new to working with complex numbers, so this was extremely helpful.