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2. Let ƒ be the branch of z¹/4 such that |z] > 0 and 0 < arg z < 2ñ. Let C denote the semi-circular path z = 2e¹0 (0 ≤ 0
Posted: Wed Jul 06, 2022 12:04 pm
by answerhappygod
- 2 Let F Be The Branch Of Z 4 Such That Z 0 And 0 Arg Z 2n Let C Denote The Semi Circular Path Z 2e 0 0 0 1 (90.36 KiB) Viewed 16 times
2. Let ƒ be the branch of z¹/4 such that |z] > 0 and 0 < arg z < 2ñ. Let C denote the semi-circular path z = 2e¹0 (0 ≤ 0 ≤ π). (a) Show that the right hand limits at 0 = 0 of the real and imaginary parts of ƒ[z(0)]z'(0) exist and calculate their values. (b) Calculate Jo (c) Why did we show that the right hand limits at 0 = 0 of the real and imaginary parts of ƒ[z(0)]z'(0) exist before calculating f(z) dz? 3. Let CR denote the circle z = Rei (0 ≤0 ≤ 2π). Show that f(z) dz. lim R→∞ JCR 2-4 (z2+1)(2³5) 1 -dz = 0