i was wondering how do you remove the modulus of a function e.g. if you had modulus of y how do you find y.
i thought you would just do the inverse of (A^2+B^2)^0.5 but i was told this was wrong?? any help would be appreciated
aorry it wasnt that great an explanation if you integrated 1/z dz=2x+4you would end up with ln|z|=x^2+4x+c then getting rid of the ln you would have
|z|=e^(x^2+4x+c) i was wondering how you would write this for z=??
Hello,
Since you talk about modulus, I assume that z is complex, then you can write $\displaystyle \ln(z)$, and this defined a value that exists.
Note that if z and z' are complex numbers, we have :
$\displaystyle \ln(z)=\ln(z') \Leftrightarrow \text{Arg}(z)=\text{Arg}(z')+2k\pi$ and $\displaystyle |z|=|z'|$
If you're talking about absolute values, and z is a real number, then you indeed have $\displaystyle \ln|z|$
So $\displaystyle |z|=e^{x^2+4x}$
Hence z can be equal to $\displaystyle +e^{x^2+4x}$ or $\displaystyle - e^{x^2+4x}$
Also, don't forget the integration constant.
You missed a step, just for the benefit of the OP...
Let's just remember that if
$\displaystyle |x| = a$ then $\displaystyle x = a$ or $\displaystyle x = -a$.
This makes sense because the modulus is really the SIZE or LENGTH or MAGNITUDE of what is inside it.
So if we had, as above
$\displaystyle |z| = e^{x^2 + 4x + C}$
we use the index law $\displaystyle a^{m + n} = a^m\,a^n$ to get
$\displaystyle |z| = e^C\,e^{x^2 + 4x}$
So $\displaystyle z = \pm e^C\,e^{x^2 + 4x}$
But since $\displaystyle e^C$ is an arbitrary constant, so is $\displaystyle -e^C$. Therefore we could write is as another letter, say A.
So $\displaystyle z = Ae^{x^2 + 4x}$.
Make sense?
Yes that's correct in essentials.
I think your teacher is just getting a bit pedantic - technically speaking if you deal with mods you have to deal with conditions, but if dealing with integration you're assumed to already know this and so can do the "inverse modding" as you say.