Complex number transpostion

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Bobby Jones

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Forgive me for this question, as it may just be a case of simply transposing the equation. Also when I write a 'w', it sybolises omega, and A1 is not A multiplied by 1, the one is a little one by his foot.

Question. By equating real parts and imaginary parts, find expressions for A1 and L in terms of A2,A3,A4,w and C

(A1+iwL)/A3 = A2/(A4 - i/wC)

Does A1 equal:

A1 = A2A3/(A4 - i/wC) - iwL


And does L eqaul:


L = A2A3/(iw(A4 - i/wC) - A1/iw


I dont have the correct software to write these formulas properly, but cheers guys for your help.
 
Bobby Jones said:
Forgive me for this question, as it may just be a case of simply transposing the equation. Also when i right a w, it sybolises the little round looking w that i think means 2pie, and A1 is not A multiplied by 1, the one is a little one by his foot.

Question. By equating real parts and imaginary parts, find expressions for A1 and L in terms of A2,A3,A4,w and C

(A1+iwL)/A3 = A2/(R4 - i/wC)

Does A1 equal:

A1 = A2A3/(A4 - i/wC) - iwL

A[sub:37ckgtr4]1[/sub:37ckgtr4] is a REAL number - why do you have 'i' in its value?

And does L eqaul:


L = R2R3/(iw(A4 - i/wC) - A1/iw

L is a REAL number - why do you have 'i' in its value?


I dont have the correct software to write these formulas properly, but cheers guys for your help.
Click to expand...
 


:idea: ? is the Greek lower-case letter Omega. If you use Window$, that letter is available in the Character Map.

Your post seems to contain a bunch of typographical errors.

You typed R2, R3, and R4 in different places; are those supposed to be A2, A3, and A4, respectively?

You also typed "in terms of A2, A3, A4, w, and C".

This means that the expression for A1 may not contain L, R2, R3, R4, or i.

Likewise, the expression for L may not contain A1, R2, R3, R4, or i.

Are these restrictions what you intended to say?

Here is your equation:

\(\displaystyle \frac{A_1 + i \cdot \omega \cdot L}{A_3} \;=\; \frac{A_2}{R_4 - i \cdot C/\omega}\)

Note that it does not contain R2 or R3 or A4.

:idea: This site provides a [Preview] button next to the [Submit] button. You can use it to proofread your posts before submitting them to the boards.

 
My apoligese for my bad posting, mmm4444bot has writen it in the correct format, except the C is underneath the division line with the omeaga, and the i is on top, so by equating real parts and imaginary parts find expressions for A1 and L in terms of A2,A3,R4, omeaga and C.


Do I need to transpose these equations for all the real parts, as A1 and L are both real. How do I do this, and what happens to the imagionary parts?
 
Does your equation then look like:

\(\displaystyle \frac{A_1 + i \cdot \omega \cdot L}{A_3} \;=\; \frac{A_2}{R_4 -\frac{i}{C \cdot \omega}}\)
 
Yes, thats it. So how would I rearange this for A1.

Will A1 equal:

A1 = (A2A3/(R4 - i/wC)) - iwL

Or should I only have the Real parts in here (the A1,A2,A3,R4), if so whast happens to the imagionary parts?

What will be the expression for L?

Please Help!
 
Subhotosh Khan said:
Does your equation then look like:

\(\displaystyle \frac{A_1 + i \cdot \omega \cdot L}{A_3} \;=\; \frac{A_2}{R_4 -\frac{i}{C \cdot \omega}}\)
Click to expand...

\(\displaystyle \frac{A_1 + i \cdot \omega \cdot L}{A_3} \;=\; \frac{A_2}{R_4 -\frac{i}{C \cdot \omega} }\cdot \frac{R_4 +\frac{i}{C \cdot \omega}}{R_4 +\frac{i}{C \cdot \omega}}\)

Now simplify.....
 


Bobby Jones said:
the C is underneath the division line with the [omega], and the i is on top

This is not what you posted.

When we want to change the famous Order of Operations while texting, we MUST type grouping symbols.

The operations of division and multiplication are done in the same order as they appear reading left-to-right.

Therefore, texting the expression i/?C shows that the division occurs first and the multiplication occurs second.

In other words, it means first divide i/? and then multiply by C; this is exactly the same as iC/?.



If the denominator is ?C, then you need to change the Order of Operations. You want to do the multiplication first, and then divide by that result.

In other words, you want i/(?C), so this is exactly what you must type.

:idea: If you ignore grouping symbols in situations like this, your typing will not represent your intent.



Do I need to transpose these equations

You have posted only one equation, thus far. How many equations did they give you? :?
Click to expand...

 


Bobby Jones said:
Will A1 equal:

A1 = (A2A3/(R4 - i/wC)) - iwL

No.
Click to expand...

They told you that the expression for A1 needs to be in terms of the symbols A2, A3, R4, ?, and C.

I already told you what this means: your expression for A1 may not contain the symbols i or L.

It seems to me that either you're not really paying much attention or you have not yet learned how to be a student. :(

 
Scary part is that this equation is from Electrical Engineering .... how shocking!!!!
 
Subhotosh Khan, I've multiplied out the complex congugate, therefore:

(A1 +iwL)/A3 = (A2R4 +((iA2)/(wc)))/(R4^2 + (1/(wc)))


Now what? Should I then take the A3 over a a multiply! but how do I "erase" the imaginary parts to equate for just the real parts.


Fellas I understand I'm not in your league of mathematics, but thats why I've turned to you, and I appreciate your help, I really do. I have no books or anyone here to help me, so bear with me if I make the odd error here and there.


Cheers guys
 
Bobby Jones said:
Subhotosh Khan, I've multiplied out the complex congugate, therefore:

(A1 +iwL)/A3 = (A2R4 +((iA2)/(wc)))/(R4^2 + (1/(wc)^2))


Now what? Should I then take the A3 over a a multiply! but how do I "erase" the imaginary parts to equate for just the real parts.


Fellas I understand I'm not in your league of mathematics, but thats why I've turned to you, and I appreciate your help, I really do. I have no books or anyone here to help me, so bear with me if I make the odd error here and there.


Cheers guys
Click to expand...

Now equate real part of the Left-hand-side(LHS) with the real part of the RHS, and,

equate imaginary part of the Left-hand-side(LHS) with the imaginary part of the RHS
 
Is this correct below for equating the real and imaginary parts. I took the A3 over, and then just took away anything with an imaginary symbol in it.(Which dosent seem right)

A1 = (A2.R4.A3) / (R4^2 + 1/(W.C))

What would L be? I got it as:

L = 1 / (w^2 .C)

Cheers Subhotosh Khan
 


Bobby Jones said:
(A1 +iwL)/A3 = (A2R4 +((iA2)/(wc)))/(R4^2 + (1/(wc)))

The denominator above in red looks wrong.



Should I then take the A3 over a a multiply[?]

I cannot determine what "over a a" is supposed to mean here, but I'm fairly certain that my answer is "no". :wink:



If you do not "see" the separate Real and imaginary parts on each side of your corrected equation, then you should probably rearrange the expression on each side using paper and pencil.

In other words, you need to view the equation in this form: a + b*i = c + d*i

When they say equate the Real parts, they mean for you to write a = c.

When they say equate the imaginary parts, they mean b = d.
Click to expand...


I will rearrange the lefthand side into the form a + b*i for you:

\(\displaystyle \frac{A_1 + i \cdot \omega \cdot L}{A_3} \; \text{is the same as} \; \frac{A_1}{A_3} + \frac{\omega \cdot L}{A_3} \cdot i\)

This rearranged expression is the Complex form a + b*i where the Real part a is the number A[sub:3al4168y]1[/sub:3al4168y]/A[sub:3al4168y]3[/sub:3al4168y] and the imaginary part b is the number ?L/A[sub:3al4168y]3[/sub:3al4168y].

Now view the righthand side as Complex form c + d*i.

After you've got it, equate the Real parts a = c, and solve that equation for A[sub:3al4168y]1[/sub:3al4168y].

If you're still confused, please ask specific questions about specific statements that you do not understand or show your work. 8-)

 
a + ib = c + id

A1/A3 + iwL/A3 = (A2.R4)/ (R4^2 + (1/w^2.C^2)) + ( iA2/(w.C)) / (R4^2 + (1/w^2.C^2))

So A1 would equate to A2.R4

and L would equate to iA2/(w.C)


Right or wrong?
 
Bobby Jones said:
a + ib = c + id

A1/A3 + iwL/A3 = (A2.R4)/ (R4^2 + (1/w^2.C^2)) + ( iA2/(w.C)) / (R4^2 + (1/w^2.C^2))

So A1 would equate to A2.R4 ..... NO!!!

and L would equate to iA2/(w.C) ..... and double NO

Right or wrong?
Click to expand...

A[sub:2bdcjfj6]1[/sub:2bdcjfj6]/A[sub:2bdcjfj6]3[/sub:2bdcjfj6] = A[sub:2bdcjfj6]2[/sub:2bdcjfj6]*R[sub:2bdcjfj6]4[/sub:2bdcjfj6]/ [R[sub:2bdcjfj6]4[/sub:2bdcjfj6][sup:2bdcjfj6]2[/sup:2bdcjfj6] + 1/(wC)[sup:2bdcjfj6]2[/sup:2bdcjfj6])] .......... and

wL/A[sub:2bdcjfj6]3[/sub:2bdcjfj6] = [A[sub:2bdcjfj6]2[/sub:2bdcjfj6]/(w.C)] / [R[sub:2bdcjfj6]4[/sub:2bdcjfj6][sup:2bdcjfj6]2[/sup:2bdcjfj6] + 1/(wC)[sup:2bdcjfj6]2[/sup:2bdcjfj6])]

.
 


Bobby Jones said:
a + ib = c + id

A1/A3 + iwL/A3 = (A2.R4)/(R4^2 + (1/w^2.C^2)) + (iA2/(w.C)) / (R4^2 + (1/w^2.C^2))
Click to expand...

The second line above is not written in the form of the first line. I think that my attempts to help have utterly failed you. :(

Earlier, I tried to explain to you why grouping symbols are crucial every time you want to change the Order of Operations while texting mathematical expressions. Maybe you did not understand my statements about this issue.

The expressions in red above are wrong because you did not type parentheses around the denominators.

Typing 1/w^2*C^2 means C^2/w^2 because we do the division FIRST.

If you want to do the multiplication FIRST, then you MUST type 1/(w^2.C^2).

I am sorry that you do not understand the concept of Order of Operations.

Right now, I'm considering that you may be one of those "students" who simply skip anything they see that does not immediately make sense to them. If this is the case, then you should know that dismissing everything that is not immediately clear to you is a very lousy way to attempt learning mathematics.

People who know how to be students always investigate statements that do not make sense to them. They accomplish this by noting words, phrases, sentences, diagrams, or entire concepts, that do not make sense when they read or hear them, and THEN they take these notes and ASK SPECIFIC QUESTIONS about each and every thing in their lessons/textbooks/lectures that they do not understand. They clear up their confusion BEFORE trying to move forward.

This much is clear: you are NOT ASKING ANY QUESTIONS about stuff that you do not understand. Instead, you make us GUESS over what you understand versus what you do not understand. Additionally, you compound this problem with sloppy communication and typing.

All of this combines to make tutoring you over the Internet very time-consuming and difficult.

I think that you are not ready to handle an exercise of this type. You clearly need classroom help. Hence, I'm suggesting that you should chat-up your instructor OR get a face-to-face tutor for intense review of the basics.

I have no more time for guessing and deciphering on your behalf, but I wish you good fortune in your future studies. Cheers ~ Mark

 
My apoligese mmm444bot. I know I'm not the greatest student. I'm just trying to give my family a better future.
 


Is the exercise in this thread your first exposure to Complex numbers?

I have since seen your post on the calculus board. I do not understand how schools allow somebody to enroll in a calculus course without knowing Complex numbers.

Are you enrolled in a calculus course?

If so, is it an on-line course?

Where are you going to school? What is your background? (I mean, how long have you been out of school?)

I would like to know more because you may be in over your head and that will not help your family.

 
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