z solutions

All z solutions to z^3=9-13i

Complex Logarithm

Given: z1 = i and z2 = -1+i Show that: Log (z1 z2) ≠ Log z1 + Log z2

Evaluating Integral Using Jordan's Lemma

The problem is to find the value of the integral from 0 to INF of [(ln x)^2]/(x^2 +9). We are to use f(z)= [(Log z)^2]/(z^2 +9), where -pi/2 < Log z < 3pi/2. We are to use the curve C from -R to -p along the real axis, -p to p around 0, p to R along the real axis, and the curve Cr from 0 to pi. I am having several probl ...continues

Evaluating an Integral

The problem is: Evaluate the integral from 0 to INF of: [(x^(1/3))*(ln x)]/(x^2 +9) dx by using f(z)= [(z^(1/3))*(Log z)]/(z^2 +9), with -pi/2 < Log z < 3pi/2. Also, with z^(1/3)= e^[(1/3)Log z]. We are to use the curve C: from -R to -p, -p to p around origin, p to R, and Cr from 0 to pi. Many thanks in advance ...continues

Evaluating an Integral With 2nd Order Pole

Problem: Evaluate the integral from 0 to INF of: (x^a)/(x^2 +4)^2 dx, -1 < a < 3 We are to use f(z)= (z^a)/(z^2 +4)^2, with z^a = e^(a Log z), Log z= ln|z| + i Arg z, and -pi/2 < Arg z < 3pi/2. I have found the residue at 2i to be: [2^a(1-a)/16]*[cos ((pi*a)/2) + i sin ((pi*a)/2). Please let me know if this is ...continues

REPOST** Evaluating an integral with pole of order 2

Earlier today I posted the problem below, and received a response which was great but it is not done in the manner that our professor wants it done. He wants us to use the branch cut of the negative Im axis, and use the following curve: C= -R to R, -p to p, p to R, and Cr from 0 to pi. Can anyone do this problem using the ...continues

How to find a power of a complex number?

Find (1+i)^100

Solve a complex variable equation.

z is a complex number, s and t are real numbers. Find z1 and z2 - the solution the solutions of the equation (z^2)+(|z|^2)-(2Is)=(8t^2) in terms of s and t. If z1*z2=-8I find s,t

Complex numbers questions

1. The equation X^5 - 2X^4 - X^3 + 6X - 4 = 0 has a repeated root at X=1 and a root at X-2. By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of X^5 - 2X^4 - X^3 + 6X - 4 (25 marks) 2. Given that cosX= (e^jx + e^-jx)/2 ...continues

Simple usage of the De-Moivre identity

Given A=(-1/2+isqrt(3)/2)^n 1. Show that A is real for any natural n 2. Show that for n=3K where K is a natural number, A=2