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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 $8z=i|z|^3\bar{z}$?
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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
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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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
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Jan
7
revised Primitive root of unity with certain conditions
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Jan
7
revised Primitive root of unity with certain conditions
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