Could you explain how to show this in detail? Given a E R, let fa(z) be the a-branch of the complex square root, that is: for every z E Csetfa(2) = Vreiarga/2 .where arga(z) is the unique angle 0 € (a, a + 27] such that z = r6.(i) Show that fm/4(2i) = 1+ i and f37/4(2i)-(1+i).{z E C : z =tea , t > 0} show that fa(z) is not continuous at any(ii) Setting Laz E La.(iii) Show that fa(z) = U(r,0) + iV(r,0) withU (r, 0) = Vr cosV (r, 0) = /r sinG).for r > 0 and a < 0 < a+2ñ, and thus that fa(z) is holomorphic on A = C\La with1fa(2) =Vz E A.2 fa(2) '

Name: Could you explain how to show this in detail? Given a E R, let fa(z) b
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Could you explain how to show this in detail? Given a E R, let fa(z) be the a-branch of the complex square root, that is: for every z E Csetfa(2) = Vreiarga/2 .where arga(z) is the unique angle 0 € (a, a + 27] such that z = r6.(i) Show that fm/4(2i)

Given, fα(z)=r ei argα/2 ..............(1) where argα(z) is the unique angle θ∈(α, α+2π]…

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Given a E R, let fa(2) be the a-branch of the complex square root, that is: for every z E C set fa(2) = Vr e' arga/ , where arga(z) is the unique angle 0 € (a, a + 27] such that z = r e?". (i) Show that fr/4(2i) = 1+ i and f3/4(2i) = -(1+ i).