TUNY, 1000ember 28, 2017, 10:30 am. 1. [6 points) what part of the plane corresp

Question

TUNY, 1000ember 28, 2017, 10:30 am. 1. [6 points) what part of the plane corresponds to the interior w-plane if: - plane corresponds to the interior of the unit cirde in the (a) w = 342? (b) w = e*? (PHYS 5041 only) (10 points) The branch cuts I only) (10 points) The branch cuts of the function f(z) = (-y Sitive integer, have been chosen to run from - to -1 along the negative real axis and from 1 to co along the positive real axis. Obtain the va the four points z = 2 + ie and -2 tie, where e is a small, positive number should take the limit as € > 0t), in the two cases: (a) p= 2 (i.e. f(z) = (22 – 1)1/2) on the Riemann sheet on which f0) = | (b) p= 3 (i.e. f(z) = (22 - 1)1/3) on the Riemann sheet on which f0) = 3. [10 points] Write the real and imaginary parts of the functions (a) f(2) = 22e; (b) f(z) = 1+z 1+z In each case use the Cauchy-Riemann conditions to determine the region of the com plex plane in which the function is analytic. For (b) compute and and use yo ulto to obtain f. Is the answer what you expected? it can only be a con

Explanation / Answer

for the given question

2. a. f(z) = (z^2 - 1)^1/2

z = +- 2 +- ie

z^2 = 4 + (ie)^2 +- 4ie = 4 - e^2 +- 4ie

f(z) = (4 - e^2 +- 4ie - 1)^1/2

f(z) = (3 - e^2 +- 4ie)^1/2

for e -> 0 +

f(z) = sqroot(3)

b. f(z) = (z^2 - 1)^1/3

z = +-2 +- ie

f(z) = (3 - e^2 +- 4ie)^1/2

hence

f(z) = cuberoot(3) for limit e -> 0+

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.