All Questions
10
questions
-2
votes
0
answers
141
views
Solving $\sqrt{x+1}=-2$ and looking for complex solutions [duplicate]
So the question was
$$\sqrt{x+1}=-2$$
And obviously there is no value for it,
However,
If you do the thing with $e$ and $\ln{}$
$$e^{\ln{\sqrt{x+1}}}$$
and
$$e^{\frac{1}{2}\cdot (\ln{x+1})}$$
Then ...
- 19
0
votes
0
answers
63
views
What are some good English mathematics exercises textbooks at the level of South East Asia high school programs?
I live in this region and is studying to retake the national test and I need a big amount of tough exercises to practice but I can't find good documents/ textbooks over here. Any appropriate textbooks ...
user1198194
2
votes
1
answer
142
views
How to solve $\ln(-2)=z$?
$$\color{white}{\require{cancel}{.}}$$So I was looking through the Youtube homepage looking for math equations that I might be able to solve and I found this video by blackpenredpen. The question was ...
- 2,652
2
votes
2
answers
72
views
What limits are there on the property that $a \space \ln(i) = \ln(i^a) $
For what values does the property $a \space \ln(i) = \ln(i^a) $ hold? I found to my dismay that $ 4 \ln(i) $ was not returning the same results as $ \ln(i^4) = 0$. In addition, does there exist a log ...
- 894
1
vote
1
answer
161
views
Simplifying an expression involving a complex logarithm
I asked WolframAlpha to solve a certain differential equation and it gave it in this form: $f(x)=(x-1)(\ln(x-1)-i\pi-1)$. Now I am only interested in this function when $x$ is in the interval $(0,1)$....
- 10.3k
4
votes
5
answers
197
views
Complex Number in a logarithm
I am having a little trouble understanding complex numbers with logarithms. How would I do the log of $e$ ($\log_{i}{e}$)? What I did firstly was to do $\frac{\log{e}}{\log{i}}$. I don’t have any idea ...
- 43
7
votes
3
answers
2k
views
Is there a trick to establish $z = \tan \left[ \frac{1}{i} \log \left( \sqrt{ \frac{1+iz}{1-iz} } \right) \right]$?
Im trying to show that
$$ z = \tan \left[ \frac{1}{i} \log \left( \sqrt{ \frac{1+iz}{1-iz} } \right) \right] $$
My first thought is to use the fact that $\sin x = \frac{ e^{ix} - e^{-ix} }{2i } $ ...
user139708
6
votes
3
answers
1k
views
What is the value of $\ln \left(e^{2 \pi i}\right)$
I know that $$e^{2 \pi i} = 1$$
so by taking the natural logarithm on both sides
$$\ln \left(e^{2 \pi i}\right)=\ln (1)=0$$
however, why isn't this $2 \pi i$ as expected? Is it beacuse logarithms ...
- 4,198
6
votes
1
answer
2k
views
How to find logarithms of negative numbers?
Logarithms of negative numbers must be complex.
But how do you find $\ln{(-2)}$ expressed in something like $x \cdot i$ where $x \in \mathbb{R}$?
- 1,319
74
votes
5
answers
5k
views
A new imaginary number? $x^c = -x$
Being young, I don't have much experience with imaginary numbers outside of the basic usages of $i$. As I was sitting in my high school math class doing logs, I had an idea of something that would ...
- 853