APPENDIX A.3 - Complex Numbers

Section A.3, page A-16

Problem 10

We want to know where |z+1| is greater than or equal to |z|. This corresponds to the real inequality:   Let's see:

>	simplify((x+1)^2+y^2-(x^2+y^2));

So we need 2x+1 bigger than 0. So the region where this is true is to the right of the vertical line Re(z)=-1/2.

Problem 24

To find square roots of i, we solve the equation:

>	solve(z^2=I);