poirot
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 Jan 19 comment How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$? Can you not use a keyhole contour? Jan 19 comment How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$? Another form is $$-\frac{1}{2}I=\int_0^\infty \frac{\sin\left(\frac{1}{2}(a+b)x\right)\sin\left(\frac{1}{2}(a-b)x\right)}{x^2}‌​{dx}.$$ Jan 19 comment Calculating $\arg(-1+\sqrt 3 \cdot i)$ To get a sense of what's going on, it can be useful to plot your complex number $-1+\sqrt{3}i$ in the complex plane. Your argument $\theta$ is then the counter-clockwise angle from the positive $x$-axis, which should give you some trigonometric intuition as to what you need to do given the quadrant within which the complex number lies, e.g. $-1+\sqrt{3}i$ is in the second quadrant, so you you know it must be $\pi/2+\phi$ where $\phi$ can be computed using trigonometry and the complex diagram. Or you could compute it using $\pi-\phi'$... Jan 17 comment Finding the result of an infinite sum Why the downvote? Jan 12 comment Finding the cartesian equation of the plane containing two given lines Find the normal to the two lines, and use $n\cdot (r-a)=0$ where $a$ is a point on the plane and $r=(x,y,z)$ is a general point. Jan 12 comment Convergence of $\int_0^{\infty}\sin (p(t))dt$ I think $p (t)=a+bt$ may be a start for investigation. Expand using trig identities. Then maybe keep adding terms e.g. $c_i t^i$ and see what happens. Jan 11 asked Can certain things never *ever* be proved? Jan 11 revised Equation in the complex plane $8z=i|z|^3\bar{z}$? added 10 characters in body Jan 11 revised Equation in the complex plane $8z=i|z|^3\bar{z}$? deleted 134 characters in body Jan 11 revised Equation in the complex plane $8z=i|z|^3\bar{z}$? added 42 characters in body Jan 11 revised Equation in the complex plane $8z=i|z|^3\bar{z}$? added 42 characters in body Jan 11 answered Equation in the complex plane $8z=i|z|^3\bar{z}$? Jan 11 comment Not getting what it means $v = ai + bj + ck$ for some vector $v$ For example, suppose you wanted to prove what $(x,y,z)+(u,v,w)$ was equal to. Well: $$(x,y,z)+(u,v,w)=ix+jy+kz + iu+iv+iw=i(x+u)+j(y+v)+k(z+w)=(x+u,y+v,z+w).$$ Ok, we intuitively know what $(x,y,z)+(u,v,w)$ is (if you've learned that somewhere), but how would go about proving it? You need to use your definitions and we define $(x,y,z)=ix+jy+kz$. Similarly we need to define what $i,j,k$ are and also what it means to write $ix$ etc. That's maths - there's no room for ambiguity ! ;-) Jan 11 answered Not getting what it means $v = ai + bj + ck$ for some vector $v$ Jan 10 comment I would like to find the value of $f(z)$ You should use the substitution $z=re^{i\theta}=r\cos\theta+ir\sin\theta\equiv g(r,\theta)+i h(r,\theta)$. Jan 10 revised I would like to find the value of $f(z)$ added 17 characters in body Jan 8 comment Prove that $a^{n+m}=a^{n}a^m$, for real numbers Could it be $e^{n\log a}$... but then what of $a\leq 0$... Jan 7 revised Primitive root of unity with certain conditions added 179 characters in body Jan 7 revised Primitive root of unity with certain conditions added 210 characters in body Jan 7 revised Primitive root of unity with certain conditions edited body