# Thread: Missundestanding of how complex numbers work not helping with fourier analysis

1. ## Missundestanding of how complex numbers work not helping with fourier analysis

I am studying electrical engineering at university level in the UK. As part of a course on Circuit and Signal processing I have tutorial sheets on Fourier Analysis.

I am fine with fourier analysis except when I start to look at exponential fourier series, I have the question, I even have the answers and how the tutor reached the answer (the workings). But I am not understanding how he is jumping from one line to another. I have attached the whole solution but the bit that I am misunderstanding is:

$\displaystyle r_{m}=\frac{-V}{4\pi^2}\displaystyle\{\frac{-1}{jm}[2\pi]\displaystyle\}$

$\displaystyle \\r_{m}=\frac{-jV}{4m\pi^2}\displaystyle\{[2\pi]\displaystyle\}$

where j = complex number $\displaystyle j^2=-1$, how is j moving from the denominator to the numerator?

surely the next line should be

$\displaystyle \\r_{m}=\frac{V}{j4m\pi^2}\displaystyle\{[2\pi]\displaystyle\}$

Any help would be greatly appreciated. Thanks Ed.

2. Originally Posted by emmv
I am studying electrical engineering at university level in the UK. As part of a course on Circuit and Signal processing I have tutorial sheets on Fourier Analysis.

I am fine with fourier analysis except when I start to look at exponential fourier series, I have the question, I even have the answers and how the tutor reached the answer (the workings). But I am not understanding how he is jumping from one line to another. I have attached the whole solution but the bit that I am misunderstanding is:

$\displaystyle r_{m}=\frac{-V}{4\pi^2}\displaystyle\{\frac{-1}{jm}[2\pi]\displaystyle\}$

$\displaystyle \\r_{m}=\frac{-jV}{4m\pi^2}\{[2\pi]\}$

where j = complex number $\displaystyle j^2=-1$, how is j moving from the denominator to the numerator?

surely the next line should be

$\displaystyle \\r_{m}=\frac{V}{j4m\pi^2}\displaystyle\{[2\pi]\displaystyle\}$

Any help would be greatly appreciated. Thanks Ed.
Now multiply top and bottom by $\displaystyle j$, this gives a $\displaystyle j$ on the top and on the bottom $\displaystyle j^2=-1$, or just $\displaystyle -j$ on the top:

$\displaystyle r_{m}=\frac{V}{j4m\pi^2}(2\pi)=\frac{Vj}{j^24m\pi^ 2}(2\pi)=\frac{-jV}{4m\pi^2}(2\pi)$

CB

3. Thanks Captain Black, to clarify my understanding:

If I had $\displaystyle \frac{1}{5}$ and I multiplied top and bottom by 5 then the answer would be $\displaystyle \frac{5}{25}$ which is still $\displaystyle \frac{1}{5}$ the actual values haven't changed just the figures representing them. So is it the case that with $\displaystyle j$ that $\displaystyle j^2$ is $\displaystyle -1$ which effectively gets lost within the other numbers?

So actually the steps are as below, but then how are you moving the minus from the denominator to the numerator?

$\displaystyle r_{m}=\frac{V}{j4m\pi^2}(2\pi)=\frac{Vj}{j^24m\pi^ 2}(2\pi)=\frac{jV}{(-1)4m\pi^2}(2\pi)$

Thanks, Ed.

4. Sorry Captain Black, I didn't think before I asked my question. If the fraction was $\displaystyle \frac{1}{-5}$ this would in fact be $\displaystyle -\frac{1}{5}$ as the minus relates to the whole of the fraction. Thank you for helping me with this. Regards Ed.