Help with transposition please

I have figured out the mesh equations for a circuit but am stuck with the transposition. The equation I havefigured out is

(jwl-j/wc)i2 - ((jwl)x(Vin+(jwL)i2) / Rs+jwL)=0

and I need to get it to equal

i2= (w^2LC) / ((1-w^2LC)Rs+jwL)

Please can you help as it has to be in tomorrow and i'm been dumbfounded for 3 weeks!!

Hi, Vicky,

I'm afraid I have more questions than answers:

I'm assuming i2 is a single variable, with 2 as a subscript. Is that right?
Are the upper- and lowercase L's and C's the same variables or different ones?
Is there more information somewhere? Your first equation has a Vin term that doesn't look like it should cancel out, but it doesn't appear in the second equation.

Also, remember that j^2 = -1.

---------------------

Update: the Vin term still doesn't cancel unless the first equation is missing parens around the denominator (Rs + jωL) like this:

(jωL - j/ωC)i₂ - [(jωL)(Vin + (jωL)i₂) / (Rs + jωL)] = 0

But then, if we multiply both sides by the denominator, we have:
(Rs + jωL)(jωL - j/ωC)i₂ - [(jωL)(Vin + (jωL)i₂)] = 0

Distribute the (jωL) in the square brackets:
i₂(Rs + jωL)(jωL - j/ωC) - Vin(jωL) - i₂(jωL)² = 0

Multiply the first term:
i₂(jωLRs + (jωL)² - jRs/ωC - j²ωL/ωC) - Vin(jωL) - i₂(jωL)² = 0

Replace j² with -1:
i₂[jωLRs - (ωL)² - jRs/ωC + L/C] - Vin(jωL) + i₂(ωL)² = 0

Move the Vin term, then factor i₂:
i₂[jωLRs - (ωL)² - jRs/ωC + L/C + (ωL)²] = Vin(jωL)

Cancel the (ωL)² terms:
i₂[jωLRs - jRs/ωC + L/C] = Vin(jωL)

Multiply both sides by ωC:
i₂[jω²LCRs - jRs + ωL] = Vin(jω²LC)

Factor Rs:
i₂[(jω²LC - j)Rs + ωL] = Vin(jω²LC)

Multiply both sides by j, remembering that j² = -1:
i₂[(-ω²LC + 1)Rs + jωL] = -Vin(ω²LC)

Rearrange:
i₂[(1 - ω²LC)Rs + jωL] = -Vin(ω²LC)

Divide both sides by the term in the square brackets:
i₂ = -Vin(ω²LC) / [(1 - ω²LC)Rs + jωL]

So either your answer or mine is off by a factor of -1.