Confusing math problem.

Maximoff · 2015-10-23 21:48:49

Hello, can someone help me to show step by step of this calculation. I get a little bit confuse for trying to solve it.

1/(R-j/ωC) = (R+j/ωC)/(R^2+1/(ωC)^2).

This is an electronic circuit consist of resistor and capacitor in series. It's about admittance.
Thank you in advance.

**sorry if this is out of topics.

bobbym · 2015-10-23 21:55:24

What are you trying to solve for?

Maximoff · 2015-10-23 22:09:48

I'm trying to solve on how from the equation at LHS can changed to equation at RHS.

From this "1/(R-j/ωC)" into this "(R+j/ωC)/(R^2+1/(ωC)^2)" .

** Y = Z^{-1}= \frac{1}{R + jX} = \left( \frac{1}{R^2 + X^2} \right) \left(R - jX\right) ---> This what I get from the internet. But somehow i don't understand it.

zetafunc · 2015-10-23 22:20:57

Just to be sure, you would like to understand why

correct? I assume you take j to be the imaginary unit, satisfying . First, understand that if we have a complex number a + jb, where a, b are real numbers, then we can multiply by its complex conjugate a - jb in the following way:

So let's apply the same idea to the LHS, with a = R, and b = . The complex conjugate of is .

So in your example, we simply multiply the top and bottom of the fraction by the complex conjugate of the denominator, which is

.

Doing so, we get:

Does this help?

Last edited by zetafunc (2015-10-23 22:21:37)

Maximoff · 2015-10-23 22:29:25

Thank you, zetafunc.

May the Force with you.

zetafunc · 2015-10-23 22:33:35

Glad I could help -- welcome to the forum. Feel free to ask if you need anything else.

Maximoff · 2015-10-23 23:06:33

Mr Zetafunc.

Sorry, but one more question. This time about the circuit but in parallel.
This time, I get a little bit confuse because when i try to use the complex conjugate is get a longer equation.

I like to understand how it change from LHS to RHS

\frac{1}{R - j\omega C R^2}{1+ (\omega C R)^2} = \frac{1}{R} + j \omega C

Thank you.

zetafunc · 2015-10-24 06:36:47

I'm sorry, but I can't understand the expression you have written. Could you try writing it here, and posting the result in this thread?

Alternatively, you could try taking the LaTeX you've posted and putting it in math tags, like this:

and tinker with it a bit using the Preview button until you get the correct expression.

Last edited by zetafunc (2015-10-24 09:14:41)

Maximoff · 2015-10-24 21:07:14

Thank you for the help, mr Zetafunc. darn, this forum is great. Math sure is fun

The equation goes like these.

I just need to understand how the LHs can change to RHS.
From the basic concept that you've shown, if I'm using the complex conjugate to solve it, it will give a much longer equation.
Hope you willing to teach me again.

*I'm been following your Youtube channel and had been learn enormously new thing. Thanks.

zetafunc · 2015-10-24 21:46:35

Thanks for typing it up in LaTeX. First, we have:

(taking the reciprocal of a fraction is the same as flipping the numerator and denominator)

(pulling out a factor of R in the denominator)

(multiplying the top and bottom of the fraction by the complex conjugate of )

(by cancelling factors and multiplying everything out at the end)

You're welcome! I'm always open to new suggestions and video requests.

Maximoff · 2015-10-24 22:45:51

Thanks, zetafunc.

Quite easy it is but to think it outside the box maybe take quite a time.

If I had some idea, i will bring it up. Thank you.

Math Is Fun Forum

#1 2015-10-23 21:48:49

Confusing math problem.

#2 2015-10-23 21:55:24

Re: Confusing math problem.

#3 2015-10-23 22:09:48

Re: Confusing math problem.

#4 2015-10-23 22:20:57

Re: Confusing math problem.

#5 2015-10-23 22:29:25

Re: Confusing math problem.

#6 2015-10-23 22:33:35

Re: Confusing math problem.

#7 2015-10-23 23:06:33

Re: Confusing math problem.

#8 2015-10-24 06:36:47

Re: Confusing math problem.

#9 2015-10-24 21:07:14

Re: Confusing math problem.

#10 2015-10-24 21:46:35

Re: Confusing math problem.

#11 2015-10-24 22:45:51

Re: Confusing math problem.

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