2bornot2b
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Questions Asked

2bornot2b:
If a, b, c be three positive numbers and a+b+c=1 then prove that
\[(a+\frac{1}{a})^2+(b+\frac{1}{b})^2+(c+\frac{1}{c})^2\ge 33\frac{1}{3}\]
 updated one year ago
 14 replies
 4 Medals
Mathematics

2bornot2b:
Person A's income is 20% more than that of person B. Calculate the percent by which B's income is lesser than A.
 updated one year ago
 1 reply
 No Medals Yet
Mathematics

2bornot2b:
What is the difference between exp(z) and \(e^z\). z is complex.
 updated one year ago
 17 replies
 2 Medals
Mathematics

2bornot2b:
Prove that
\[\huge{(e^w)^z=e^{[(w+2ni\pi)(z)]}}\]
but \[\huge (e^w)^z\ne e^{(wz)}\] where w and z are complex.
 updated one year ago
 28 replies
 No Medals Yet
Mathematics

2bornot2b:
Can someone explain why the last equality is possible?
\[\large{a^b=(re^{i\theta })^b}\]\[\large{=(e^{ln~r+i\theta})^b=e^{(ln~r+i\theta)b}}…
 updated one year ago
 27 replies
 3 Medals
Mathematics

2bornot2b:
\[\huge{a^b=e^{b~Loga}}\]
Here a and b are complex numbers.
This is the definition of complex exponent. Why is it defined so?
 updated one year ago
 26 replies
 2 Medals
Mathematics

2bornot2b:
How do we figure out what is going to be the domain of the log function for complex numbers? It is easy to figure out for inverse trigonomet…
 updated one year ago
 13 replies
 1 Medal
Mathematics

2bornot2b:
How many members of the set S={x:1≤x≤100} are of the form 4n1. I guess the answer is 25, but is there a way to prove it or show it?
 updated 2 years ago
 4 replies
 5 Medals
Mathematics

2bornot2b:
If \(a_1, a_2,...a_n\) is a complete set of residues modulo \(n\) and \(gcd(a, n)=1\), then prove that \(aa_1, aa_2,...aa_n\) is also a com…
 updated 2 years ago
 8 replies
 2 Medals
Mathematics

2bornot2b:
If \(d=gcd(a,b)\), then show that \(gcd(a^2,b^2)=d^2\)
 updated 2 years ago
 13 replies
 2 Medals
Mathematics

2bornot2b:
If gcd(a,b)=1 then prove that gcd(ac,b)=gcd(c,b)
 updated 2 years ago
 7 replies
 4 Medals
Mathematics

2bornot2b:
Prove that if an integer is a perfect square and a perfect cube, simultaneously, then it is either of the form 7k or 7k+1
(The problem belo…
 updated 2 years ago
 8 replies
 2 Medals
Mathematics

2bornot2b:
Prove that the product of 4 consecutive integers is 1 less than a perfect square.
 updated 2 years ago
 5 replies
 4 Medals
Mathematics

2bornot2b:
Show that an integer of the form 6k+5 is also of the form 3k+2, but not conversely
 updated 2 years ago
 8 replies
 1 Medal
Mathematics

2bornot2b:
What is the difference between a Fibonacci sequence and a Lucas sequence?
 updated 2 years ago
 3 replies
 1 Medal
Mathematics

2bornot2b:
Once again, OpenStudy signs me out, every time I leave it.
 updated 2 years ago
 1 reply
 4 Medals
Mathematics

2bornot2b:
What exactly happens when I click the red "Block User" button?
 updated 2 years ago
 1 reply
 6 Medals
Mathematics

2bornot2b:
So can't we delete our own questions any more?
 updated 2 years ago
 7 replies
 8 Medals
Mathematics

2bornot2b:
What is the difference between the terms denumerable and enumerable.
 updated 2 years ago
 16 replies
 1 Medal
Mathematics

2bornot2b:
What are Cauchy’s first and second limit theorems?
 updated 2 years ago
 20 replies
 3 Medals
Mathematics

2bornot2b:
There seems to be a problem. I appear to be a mod in the English group, even though there are several users out there, higher levelled than …
 updated 2 years ago
 4 replies
 6 Medals
Mathematics

2bornot2b:
I am trying to solve the following problem, and I have a solution which I don't understand, can you help me?
"Show that in a triangle the p…
 updated 2 years ago
 20 replies
 1 Medal
Mathematics

2bornot2b:
I am trying to solve the following problem, and I have a solution which I don't understand, can you help me?
"Show that in a triangle the p…
 updated 2 years ago
 13 replies
 1 Medal
Mathematics

2bornot2b:
Evaluate the integral \[\int\frac{1}{(x^2\sqrt{x^216)}}dx\] using the substitution \[x=4\sec\theta\]
This question is originally posted …
 updated 2 years ago
 14 replies
 6 Medals
Mathematics

2bornot2b:
Does it help in any way, to think of sequences as countable subsets of the Real numbers? Does this way of thinking take us anywhere importan…
 updated 2 years ago
 2 replies
 2 Medals
Mathematics

2bornot2b:
Does it help in any way, to think of sequences as countable subsets of the Real numbers? Does this way of thinking take us anywhere importan…
 updated 2 years ago
 3 replies
 1 Medal
Mathematics

2bornot2b:
What is the significance of the phrase "non empty"?
 updated 2 years ago
 28 replies
 1 Medal
Mathematics

2bornot2b:
If while replying, I am attaching a file to one particular post, its getting carried to all the posts (made by me) in that thread. Is that h…
 updated 2 years ago
 3 replies
 1 Medal
Mathematics

2bornot2b:
Why is the approximation theorem of supremum called so? I mean why is it named "approximation theorem"?
 updated 2 years ago
 13 replies
 3 Medals
Mathematics

2bornot2b:
Why is the approximation property of supremum called so
 updated 2 years ago
 2 replies
 No Medals Yet
Mathematics
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