Recent content by MadCow999

Huzzah! i can see clearly now(!)... thanks a bunch! now (hopefully) i can apply that stuff in my homework problems!

Homework Statement Integral from 0 to 2*pi of [(Cos(3*theta)) / (5 - 4Cos(theta))] (d*theta) Homework Equations z=exp(i*theta), Cos(theta) = (z + z^(-1)) / 2, Cos(3*theta) = ((exp(3*i*theta)+exp(-3*i*theta)) / 2 = (z^(3) + z^(-3)) / 2, dz = (i*z) (d*theta) The Attempt...

okiedokie thanks!

hmm. so it seems to work if 'z.' = 0, but how can i say that? same goes for R = 1 is it because z. is just some arbitrary point i can pick? we've done integral of (1/z)*dz, where z= R(exp(i*theta)) and dz = R*i(exp(i*theta))d(theta) that comes out to be 2i*pi, but we were also doing over the...

Homework Statement Let C. denote the circle |z-z.|= R, taken counter clockwise. use the parametric representation z= z. + Re^(io) (-pi </= o </= pi) for C. to derive the following integration formulas: integral C. (dz/(z-z.)) = 2ipi Homework Equations note: z. and C. represent z knot...