Complex Analysis Answers

Use the method of contour integration, evaluate the integral ∫02πcos3θ/5−3cosθdθ.

solve (x^3+3xy^2)p+(y^3+3x^2y)q=(x+y)^2z

Complex conjugate of function z, if z=5+3i?

What is the value of zbar(z) if w ehave z=2+3i?

Calculate the Argument of z, where z= 2+3i

We adopt the following notation: N and L indicate respectively the total number of

nodes and links of the network, Air indicates the generic element of the adjacency

matrix A of the network, ki

indicates the degree of node i and hki indicates the

average degree of the network.

At time t = 1 the network is formed by a n0 = 6 nodes m0 = 6 links.

At every time step t > 1 the network evolves according to the following rules:

- A link (r,s) between a node r and a node s is chosen randomly with uniform

probability

π(r,s) = Ar,s/L

and is removed from the network.

- A single new node joins the network and is connected to the rest of the network

by m links with m fixed to a time-independent integer constant satisfying

2 < m ≤ 6. Each of these new links connects the new node to a generic node j

chosen with probability

Πj =kj/(k)N

.a) Evaluate Π˜

i(t) indicating the expected increase in the number of links of node i

at any given time t and show that it follows the preferential attachment rule.

The inverse point of 1+i with respect to the circle |z-1|=2 is

DX/x+y=dy/x+y=DX/-(x+y+2z)

Mod of 2+3i

n an expression 2[2+2{39-2(17+2)}], which part has to be simplified first