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Jan
19
comment Name for “3D quadrilateral” shape?
Just found this: I think maybe polyhedron might cover it (in general). A polyhedron with 6 faces is called a hexahedron. mathworld.wolfram.com/Hexahedron.html
Jan
19
revised Name for “3D quadrilateral” shape?
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Jan
19
asked Name for “3D quadrilateral” shape?
Jan
19
revised How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
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Jan
19
answered How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
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 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 $8z=i|z|^3\bar{z}$?
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Jan
11
revised Equation in the complex plane $8z=i|z|^3\bar{z}$?
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Jan
11
revised Equation in the complex plane $8z=i|z|^3\bar{z}$?
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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 $f(z)$
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