Find the argument of z = (6 + 5i)20 on the principal branch, i.e. Arg z.

Find the argument of z = (6 + 5i)20 on the principal branch, i.e. Arg z.
Problem 5: Let f(z) = zi = eiLog?, [2] > 0, -T < Arg z <a denote the principal branch of the function z', and let C be any contour from –2 to 1 that, except for its endpoints, lies above the real axis. (a) Find an antiderivative of the function f(z); (b) Compute the integralf(z)dz; SOLUTION:
2. Let f(z) be the principal branch of i.е., f(z) exp@ Log(z)}. Co mpute (e)dz where C is the semicircle {et : 0 < θ < π
Let p(z) be the principal branch of 21-i. Let D* = C\(-00,0) be all the complex numbers except for the non-positive real numbers. (a) (4 points) Find a function which is an antiderivative of p(x) on D". (b) (6 points) Let I be a contour such that (i) I is contained in D* and (ii) the initial point of I' is 1 and the terminal point of I is i. Compute (2)dr. Justify your answers.
Complex
6. Find a branch of the multiple-valued expression f(z)-log(i(z + 21)) which is analytic for all z in the open disk
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute [flade, where (a) (2 points) y is the upper half of the unit circle C(0) from +1 to -1; (b) (2 points) y is the lower half of the unit circle C1(0) from +1 to -1.
[3] Let p(z) be the principal branch of 21-1. Let D* = C\(-0,0] be all the complex numbers except for the non-positive real numbers. (a) Find a function which is an antiderivative of p(z) on D*. (b)Let I be a contour such that (i) T is contained in D* and (ii) the initial point of is 1 and the terminal point of I is i. Compute J, Plzydz. Justify your answers. [9] Let f(z) be the function 2 3 f(x)...
1. (20 points) Let C be any contour from z = -i to z = i, which has positive real part except at its end points. Then, consider the following branch of the power function zi+l; f(3) = 2l+i (1=> 0, < arg z < Now, evaluate the integral Sc f(z)dz as follows: (a) (5 points) First, explain why f(z) does not have an antiderivative on C, but why the integral can still be evaluated. (b) (5 points) Then, find...
Find the Im(w)where w is the positive solution to z2 =6+5i
Find A* for the following matrix A: A= =( -3-12i 3 - 10i 6-5i -4+ 7i
Vector A⃗ =2i^+3j^ and vector B⃗ =5i^−5j^+4k^. Find: (1). X component (2). Y component (3). Z component