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I think that you have the correct residues at $z = -2\pm5i$. The residue at $z=3$ is wrong. It should be $$\left.\frac d{dz}\,\frac{e^{iz}}{z^2 + 4z + 29}\right|_{z=3},$$ which I get to be $\dfrac{(5i-1)e^{3i}}{250}.$Doomknightx9 said:
Complex numbers integrals are integrals that involve complex numbers as variables or constants. They are used in complex analysis to calculate line integrals, contour integrals, and other types of integrals that involve complex numbers.
Complex numbers integrals are evaluated using techniques from complex analysis, such as the Cauchy-Riemann equations, Cauchy's integral theorem, and the residue theorem. These techniques allow for the conversion of complex numbers integrals into real-valued integrals that can be solved using traditional methods.
Complex numbers integrals are important in mathematical and scientific applications that involve complex numbers, such as quantum mechanics, electromagnetism, and fluid dynamics. They also have practical applications in engineering, physics, and other fields.
Yes, complex numbers integrals can have imaginary values. This is because complex numbers have both real and imaginary components, and their integrals can involve both types of components. In fact, complex numbers integrals can have a combination of real and imaginary values.
Yes, there are several special properties of complex numbers integrals. For example, the Cauchy integral formula states that the integral of a function over a closed contour is equal to the sum of the function's values at the points inside the contour. Additionally, the residue theorem allows for the evaluation of complex numbers integrals using the residues of a function at its singular points.
