last class we spent a lot of time showing you guys that directional angle remember the linear combination of V equals cosine of theta * I plus s of theta * J I did that whole explanation to really figure out that the tangent of theta equals B over a right it's minus thank you all right so first of all let's just go back to the magnitude it says what is first the magnitude of V well the magnitude of V remember is V1 2 + v2^ 2 now remember when something's written in linear in linear combination this is the same thing as V equals V1 I plus V2 I or v2j so therefore if I say what's my V1 and my V2 my V1 is the coefficient six and my V2 is my coefficient of J which is -6 so therefore I'm going to have square otk of 6 2+ -6 2 right you're not putting the I's and the J's in there it's only the coefficients it's V1 * I plus V2 * J therefore I'm going to get the square root of 72 right and then I need to see how can I simplify that um any further so now I need to figure out what is the largest square number that can divide into 72 that I can figure out to simplify eight and nine no there should be maybe even higher 12 12 and six very good so well 12 and six is neither of them are going to be a square number though right but we can simplify that even further so let's just do 12 and six can I simplify now um 12 yeah you can break this down into uh the sare < TK of 4times theare > of 3 time the sare < TK of 6 square of 4 is 2 * the of 18 can I break down the square Ro of 18 yeah did nine and two right so if we were done this the other way what you guys could notice is 72 could be broken down ladies and gentlemen into 36 * 2 right which gives us our same answer but it's okay if you can't think of 36 if you can just think of unnumbered to do that's fine but you're just going to have to do a couple extra steps okay there's nothing wrong with doing it this way if you can't figure out the final answer but 36 would have been the best answer for us to choose that divides into there right but if you can't think of it and you think of 12 and six then do it but but you can still simplify that further does that make sense okay so we have 6 comma radical 2 so that's the magnitude so there's your magnitude then ladies and gentlemen the next thing it says is find the directional angle well remember the direction of the angle is just your tangent of th is equal to b a right direction of an angle equals tan of th which is equal to B over a where B kind of represents your V2 and a represents your V1 so we say tan of theta equal 1 therefore Theta equal tan inverse a 1 so now we do the tangent of1 and we should get - 45° we get - 45° so therefore if we're going to look at our Circle we have 45° in the negative direction right but we want to figure out the positive direction so if this is Theta or this is our reference angle 45° our Theta not Q is going to equal 315° so therefore we can say Theta is going to equal 35 de okay because we'll use the positive form of our angle magnitude Direction okay that's all you had to do you have to dra little no no I I just did that to help