# How to calculate the magnitude of a function?

by seto6
Tags: function, magnitude
 P: 251 1. The problem statement, all variables and given/known data I have this function: G(w)=$\frac{1}{j\omega\tau+1}$ I want to find the magnitude 2. Relevant equations S=$\alpha$+j$\beta$ magnitude(S)=$\sqrt{[itex]\alpha$^{2}+$\beta$^{2}}[/itex] [b]3. The attempt at a solution[/b What i did was carry out the division, so i got $\frac{j\omega\tau-1}{-(j\omega+1)}$ then do i just split it into real and imaginary part and then take the magnitude using this? S=$\alpha$+j$\beta$ magnitude(S)=$\sqrt{[itex]\alpha$^{2}+$\beta$^{2}}[/itex] Can anyone help i am not so sure how to approach this?
P: 339
 Quote by seto6 What i did was carry out the division, so i got $\frac{j\omega\tau-1}{-(j\omega+1)}$
This is where you got it wrong. Try to multiply the numerator and the denominator of the original G(ω) by $- j ω \tau + 1$ and see what you get.
 P: 339 Then, try and think what you had to multiply by the expression $- j ω \tau + 1$ to get your answer.
 Quote by seto6 1. The problem statement, all variables and given/known data I have this function: G(w)=$\frac{1}{j\omega\tau+1}$ I want to find the magnitude 2. Relevant equations S=$\alpha$+j$\beta$ magnitude(S)=$\sqrt{[itex]\alpha$^{2}+$\beta$^{2}}[/itex] [b]3. The attempt at a solution[/b What i did was carry out the division, so i got $\frac{j\omega\tau-1}{-(j\omega+1)}$ then do i just split it into real and imaginary part and then take the magnitude using this? S=$\alpha$+j$\beta$ magnitude(S)=$\sqrt{[itex]\alpha$^{2}+$\beta$^{2}}[/itex] Can anyone help i am not so sure how to approach this?
Failexam's suggestions are all you need to do. However, if you are going to use LaTeX, why not do it properly? Your expression for "magnitude(S)" is ugly; here is what it should look like: $\text{magnitude}(S)=\sqrt{\alpha^2 + \beta^2}.$ To get this, just remove the "inner" [i t e x]-[/i t e x] pairs; furthermore, if you want the word "magnitude" to appear in nice text font, just include it inside the [i t e x] command, but say \text{magnitude}.