Intereting Posts

Is Minimax equals to Maximin?
Which is bigger: $(\pi+1)^{\pi+1}$ or $\pi^{\pi+2}$?
Is it known if $\pi + e$ is transcendental over the rational numbers?
Representation of quiver $1 \to 2 \to 3$
Definition of the $\sec$ function
Reference Request: Finding an Op-Ed by J. Hammersley
Flip a coin until a head comes up. Why is “infinitely many tails” an event we need to consider?
Integral of alternating series
Inverse of composition of relation
Confused about why “disjointifying” implies “AC”
Help proving the primitive roots of unity are dense in the unit circle.
Solving Equation through inequalities.
differentiate log Gamma function
Consequences of cycle space cut space duality
FOUR-algebra – boolean algebra?

I am supposed to integrate $f(z)=$$\frac{5}{z}$ from -3 t0 3 but I am having trouble understanding how to do this. I’ve done the integration the “hard” way by using parametrizations but now I need to use the fact that $f(z)$ is analytic everywhere except at $z=0$ and a different method to perform the integration but I am stumped.

- Show that $\int_0^\pi \log^2\left(\tan\frac{ x}{4}\right)dx=\frac{\pi^3}{4}.$
- Trying to evaluate $\prod_{k=1}^{n-1}(1-e^{2k\pi i/n})$ for my complex analysis homework
- Principal part of Laurent expansion.
- Sheaves and complex analysis
- Contour Integration - my solution for real integral is complex?
- Inequality for incomplete Gamma Function
- Does $|f|$ locally constant imply $f$ constant globally?
- Does convergence of power series on radius of convergence imply absolute convergence?
- Multiple Integral $\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\frac1{1-xyzw}\,dw\,dz\,dy\,dx$
- Determine all the values of $1^{\sqrt{2}}$

There is not quite enough information to answer this question, although you can narrow it down a bit. For example, all paths that stay in the upper half plane will give the same answer, which will be the same as if you go along the upper semicircle: $C: z(t) = 3e^{it}, \pi \geq t \geq 0$

$$\int_C \frac{5}{z}dz = \int_\pi^{0} 5\frac{3ie^{it}}{3e^{it}}dt = -5\pi i $$

If the path is completely in the lower half plane, the answer will be the same as integrating along the lower semicircle. $C: z(t) = 3e^{it}, \pi \leq t \leq 2\pi$

$$\int_C \frac{5}{z}dz = \int_\pi^{2\pi} 5idt = 5\pi i $$

There are some other weird paths that give any value of $5\pi i + 10n\pi i$. For example, if circle the origin clockwise $n$ times and then hit 3, the value will be $5\pi i – 10n\pi i$

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- Show that every group of prime order is cyclic
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- How many groups of 4 primes exist such that their sum is a prime and that $p^2+qs$ and $p^2+qr$ are squares?
- The Ring Game on $K$
- What is an example of pairwise independent random variables which are not independent?
- Examples of non-measurable sets in $\mathbb{R}$
- Partial vs Total Derivative (Basic)
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- a spider has 1 sock and 1 shoe for each leg. then find out the the total possibilities.
- Find Total number of ways out of N Number taking K numbers every M interval
- Equivalence of two characterizations of the norm of an algebraic integer.
- Why does minimizing $H =\sum^{N}_{i=1}(y_i-f(x_i))^2+\lambda \| Pf \|^2 $ leads to solution of the form $ f(x) =\sum^N_{i=1}c_iG(x; x_i)+p(x)$?
- Find all integer solutions to linear congruences