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Problem 4. b + cz Let Res(f, zo) be the residue of f(2) at zo. If f(x) 10Res(f, 1) + Res(f,0). 22 -, find 2 Your answer Problem 5. Refer back to the last question. Let p be the remainder when b is divided by 3. Let Co be the circle [2] = {. Let C be the circle 12 – 11 = {. Let C2 be the circle 2 – 3 = 42. What is f(2) dz? 1 mi πι Cp Your answer
Which of the following are not Consider, f(2)= true for f(z)? za btc • f(2) has a singular point at a +b-c. ,2 - . • f(2) can be expanded into a Taylor series about 2= a + b - c. f(2) can be expanded into a Laurent series about z= a + b - c. . Option 1 Option 2 Option 3 Option 4 Problem 7. Let p be the remainder when c is divided by 3. If you expand 1 into a Laurent series valid for z1 < 1, then the coefficient (1+x)(3+2) is r. What is the closest integer to 1000r? of 2P+3 Your answer
a + x2 dx. By a+22 Consider the improper integral 12 1 + x4 inspection of the integrand, we see that the corresponding complex- valued function f(2) has two poles in the upper half 1 + 24 plane at 21 = e 7 and 22 = e. If R1 and R2 are the residues at 21 and 22 respectively, then find the closest integer to 21i(R1 + R2). 3mi Your answer Problem 9. Refer back to the last question. Find the closest integer to 12. Your answer