# Parametric Complex Valued Curves

BEMath shared this question 4 years ago

I wish to be able to graph the complex solutions to a real valued function on two different planes, with the real values on the xz plane and the imaginary values on the yz plane. This is what I have tried:

Real Values:

Curve[real(ComplexRoot[t²

+ 1]),

0, t, t, -20, 20]

Imaginary Values:

Curve[imaginary(ComplexRoot[t²

+ 1]), t, 0, t, -20, 20]

As far as I can tell, ComplexRoot is required to return complex as well as real roots of an equation. Is there a better way to ensure that the values returned are complex?

Thanks! --Ben

(I am reading the book "Elliptic Tales" and decided that I finally wanted to be able to see all the roots together.)

1

I was able to graph these as the trace of the complex solutions. You can see the results here:

I am still interested a more robust way to do this. Any suggestions would be appreciated!

1

Maybe hide the roots if they are real? eg put this in Condition to Show Object

1. real(a)==0