Question

In this exploration, you will investigate the behavior of systems of differen tial equations in the complex plane of the form z = F(2). Throughout this section, z will denote the complex number z x+ iy and F(2) will be a poly- nomial with complex coefficients. Solutions of the differential equation will be expressed as curves z(t) x(t) iy(t) in the complex plane You should be familiar with complex functions such as exponential, sine, and cosine, comprehend fully what you see in the following. Theoretically, you should also have a grasp of complex analysis as well. However, al of the rou- tine tricks from integration of functions of real variables work just as well when integrating with respect to z. You need not prove this, for you can always check the validity of your solutions when you have completed the integrals as well as with the process of taking complex square roots, to Classify all complex quadratic systems of the form where a,b C

Answer 1

Guren quatnatic sy사ans 아 thL toum .z-zaztb. Sinee evy poly nowd al 서plit into tnean tacton lo a pbe noot .. z' -lz-p) tP -a ap 2-e 2 P Z-A 2-)(2-A) c e Z-o nteatay Comstant in whu e A fn the collechHon t (z-) (z-p) = c e complex quaadratic system