Residues : Calculate the Integral

Calculate the following integral: ∫ 0-->2pi e^(e^iθ) dθ Please see attached for full question.

Residues and Closed Contours : Solve the Integral

Calculate the following integral... Please see attached for full question.

Integral of a Contour

Calculate the following integrals: ∫ from 0 to ∞ x^¼/(x²+9) dx Please see attached for proper format.

Complex Conjugates

What is the complex conjugate of 78.93iw^3+30.48iw^2+iw? How did you find it?

Solve the Complex Number Equality

Please show me how to solve the following : x^4 = 5 - 5i

Investments : Amount of a Fund that can be Spent Each Year

If I invested $100,000 now at 12% per yr over 15 yrs what if the most I could spend in equal amounts out of the fund each year? Please also show the formula as to how this was calculated.

Proof of Trignometric Relationship Using Complex Numbers

Given that cos x=(e^jx + e^-jx)/2 and sin x=(e^jx - e^-jx)/2j Using ONLY this information, prove that: cosAsinB=1/2[sin(A+B)- sin(A-B)]

Find roots and solve a quadratic equation given two complex conjugate roots.

The equation {see attachment} 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 ... {see attachment}

In the following equation, by equating real and imaginary parts, find the values of X & Y

In the following equation, by equating real and imaginary parts, find the values of X & Y (3+j7) = square root of {(X+j5Y)/ (6+j)}

Show that the derivative of the following function does not exists at any point f(z) = 2x + ixy^2 Note that I and j are used and they represent the same imaginary quantity ( – 1)^(1/2).

Complex Variables Existence of a Function Show that the derivative of the following function does not exists at any point ...continues