## Basic Circuit Analysis - mutual induc

This problem seems so simple, but I CANNOT get the right answer.

Here is the work I've done so far:

I've also attached the work, but if anyone wants to check the links before it gets approved, please be my guest.

The books says that the correct answer is:

V0 = 2.24 at an angle of -153.43

I don't understand what I'm doing wrong !
Attached Thumbnails

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 Not exactly the most helpful tip, but you will get the answer in the book (according to the method you used) if the mutual inductance is 2j instead of j.
 I think you mixed the inductance in your equations. I agree with doodle, if you use j2 you'll get the answer in the back of the book.

## Basic Circuit Analysis - mutual induc

Why would the mutual inductance term be 2j?

Isn't M defined by as $j1\omega$ ?

If I use 2j I get the book's answer, but I don't understand why I should use 2j.

 I am not sure why you should say that M is defined as j1w. Or perhaps you are trying to say that the question explicitly gave M = j1w? A quick browse in my Circuit Theory textbook reveals that M depends on the coupling coefficient, k, and then M = k sqrt(L1*L2).
 Oh sorry about the latex confusion. Yes, the question explicitly said that $M = j1\Omega$ I typed a small omega instead of a big one.