Convert H(F) = 5/(1+j2πF/10) to polar form with magnitude and phase

[amiv4]

Homework Statement

H(F) = 5/(1+j2piF/10)

Rewrite in polar form, that is, in terms of magnitude and phase.

Homework Equations

The Attempt at a Solution

phase is the 2piF/10 but I'm not sure how I account for it being on the bottom of the fraction

 

[xcvxcvvc]

$$\frac{ A \angle \theta}{B \angle \phi} = \frac{A}{B} \angle \theta - \phi$$also "2piF/10" is not the phase, not even for the complex number in the denominator alone.

to find an angle, you think of it in terms of real and imaginary parts forming a right triangle on the unit circle. The angle is this:
$$\arctan\frac{Im(A \angle \theta)}{Re(A\angle \theta)}$$

 

[amiv4]

So I should convert the top and bottom to polar separately and then divide them?

 

[xcvxcvvc]

So I should convert the top and bottom to polar separately and then divide them?

we must be careful when you ask questions with so many undefined pronouns. If by them, you mean the magnitudes and if you meant "should i ... to find the resultant magnitude", then the answer is yes.

if you are talking about angles, however, the answer is no. you must subtract the denominator's angle from the numerator's angle to find the resultant angle.

 

[amiv4]

k this is what i got

5$$\angle$$0$$/$$1.18$$\angle$$32.14

but idk where the F goes

 

[xcvxcvvc]

k this is what i got

5$$\angle$$0$$/$$1.18$$\angle$$32.14

but idk where the F goes

the f remains symbolically.

for example, the magnitude of the bottom vector is:
$$\sqrt{1^2 + (\frac{2piF}{10})^2}$$

 

[amiv4]

and then I would do the arctan of those two things to get the angle, but I don't see how they are going to simplify. Cuz I have to use this answer. Is there a way I could get the answer into a form similar to this H(F)=|5F| exp(-jpiF/10)

 

[xcvxcvvc]

and then I would do the arctan of those two things to get the angle, but I don't see how they are going to simplify. Cuz I have to use this answer. Is there a way I could get the answer into a form similar to this H(F)=|5F| exp(-jpiF/10)

it doesn't need to simplify. it will be messy but correct. as for putting it in the form you've specified:

$$A \angle \theta = Ae^{j\theta}$$
and your theta for the overall transfer function will be:
$$\theta = -\arctan \frac{\pi F}{5}$$

the negative comes from 0 - stuff