(z] > 0, 0 < arg z <2π); al 2. Show that 71/4 z=-1 z+1 Log z = 1+i √2 л+2i (a) Res (b) Res = 8 1-i (c) Res = z=i (z² + 1)² 8√√2 z=i (z² + 1)² z1/2 (z > 0,0

Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

The Wronskian for the fundamental Set of Solutions to the DE ty'" + 2y"-y'+ ty=0 is a) ct². b) ct^-2 c) ct d) ct^-1

How can I find a formula for the coefficient of z^k in (ab)(z)?

true or false In the domain of Gaussian integers Z[i], the element 17 is Irreducible

Determine which of the equations below could be the class equationgiven in the proof of Theorem 24.2. For each part, provide yourreasoning.a. 9 = 3 + 3 + 3b. 21 = 1 + 1 + 3 + 3 + 3 + 3 + 7c. 10 = 1 + 2 + 2 + 5d. 18 = 1 + 3 + 6 + 8

1. Find the natural cubic spline sN (x) passing through the 3 points (xj, yj) given by (0, 2), (2, 3), and (3, 1).Then evaluate sN (1).

Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of the equation yn + 1 = yn + hf(xn, yn) by hand, first using  h = 0.1  and then using  h = 0.05. y′ = x2 + y2, y(0) = 3;   y(0.5)

Let z=3+7i and w=7−8i . Find out the following in the x+iy form. z2 + w zw2