solving quadratic by process of division and finding all roots and then the factors

The equation x - 18x + 121x - 368x + 420=0 has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of : x - 18x + 1 ...continues

The problems are from stat class, 400 level course.

a. Test is the difference in lifetime of vehicles exist between the two manufacturers at a=0.01. Please see attached.

Analytic Functions; Harmonic Functions; Laplace's Equation

5. Let the function ... be analytic in a domain D that does not include the origin ... 13. ... state why the functions ... are harmonic in D and why ... is in face, a harmonic conjugate 11. ... Why must this satisfy Laplace's equation? Please see attachment for complete questions. Thanks.

Proving ∑ 1/(n^2) = (Pi^2)/6 using Cauchy's Residue Theorem

Deducing that ∑ 1/(n^2) = (Pi^2)/6 is a classic problem in Mathematics. Often it is demonstrated by using Fourier series, but it can also be proved by using Cauchy's Residue Theorem.

Review: Arc, Cauchy-Goursat Theorem, Integral, Paratmetric Representation etc.

Please assist me with the attached problems, such as: 1. Without evaluating the integral show that (see attachment) when C is the same arc as the one in Example 1 (see attachment for example)

Review: Log, Roots, Continuous Complex-Valued Function, Mean Value Theorem etc.

Please assist with the attached problems, such as: 4. By chooseing specific nonzero values of z1 and z2, show that ... is not always valid when log is replaced by Log.

Evaluating Integrals by Cauchy-Goursat Theorem

Evaluating integrals by Cauchy-Goursat Theorem. See attached for full problem description.

Three problems.

2. Suppose that f(z) is entire and that the harmonic function... Show that u(x,y) must be constant throughout the plane... See the attachment for all problems.

two problems.(Complex variables)

2. Derive the Laurent series representation... Please see attached.

complex variables (evaluation problems).

See the attachment for the problems. Thank you