2 complex intergrations

  • #1
1. Evaluate ∫C (z)/z2+9 dz , where C is the circle │z-2i│=4.

what i have done so far is :

z(t) = 2i + 4eit
z'(t) = 4ieit
f(z(t)) = 4ieit/(4ieit)2+9

∫ (4ieit/(4ieit)2+9) (4ieit) dt

intergrate from 0->2pi

but i dont know how to solve this intergral, can anyone help?

2. ∫c cos(z)/(z-1)^3(z-5)^2 dz , where C is the circle │z-4│=2.

this z'(t) = 0
so , is this intergral equal 0?
since f(z(t))(z'(t)) = 0


Thanks
 

Answers and Replies

  • #2
121
0
Shouldn't you be using the residue theorem to evaluate the integrals?

(Note that (1) has poles at ±i3, and (2) has poles at 1 & 5. Which of those lie within the given contours?)
 

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