definite integral

Evaluate the integral from 0 to infinity of X^2/(X^4+2X^2+1) dx

integral

Evaluate the integral from 0 to inf. of [cos(3x)-cos(5x)]/x^2 dx

Integral of a hard polynomial

Suppose that p(z) and q(z) are polynomials with a complex coefficients with the property that deg q(z) is greater than or equal to deg p(z)+2. If C is a positively oriented simple closed contour containing all of the roots of q(z) on its interior, then prove that integral C of p(z)/q(z) dz = 0

Uning the Euler's identity to calculate the root of i

Calculate the square root of i using a direct method and show that using Euler's formula yield the same result.

f(x,y) algebra equation

I am looking for a software package that can solve simple random equations like f(x,y) as an "input" and plot the 3-D results as the "output" using x, y and jx. My object is to view both real and imaginary parts of the graph on one x, y and jx 3-D coordinate system while using y as the independent variable. Complex math soft ...continues

Complex Variables: Associative and Commutative Laws for Multiplication

3. Use the associative and commutative laws for multiplication to show that: (z1z2)(z3z4) = (z1z3)(z2z4) 4. Prove that if z1z2z3 = 0, then at least one of the three factors is zero. *Please see attachment for proper citation of equations (they did not transfer over into the text box properly)

Complex Variables: Verify Inequality

3. Verify that (sqrt(2))ּ|z| ≥ |Re z| + |Im z|. Suggestion: Reduce this inequality to (|x| - |y|)2 ≥ 0. Sqrt(2) means square root of 2.

Complex Variables: Sketch Points Determined by Given Condition

4. In each case, sketch the set of points determined by the given condition: (a) |z -1 + i| = 1 (b) |z + i| ≤ 3 (c) |z -4i| ≥ 4

Complex Variable: Using Established Properties of Moduli ...

7. Use established properties of moduli to show that when |z3| ≠ |z4|, |z1 +z2| / |z3 + z4| ≤ ( |z1| + |z2|) / | |z3| - |z4| |.

500 level complex variable in undergraduate

The problems are from complex variable 500 level in undergraduate. Please specify your notation(if necessary) and explain clearly each step of your solution. Thank you very much.