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Solve each equation and check the result. $$37.1 w+12.2=16.8 w+93.4$$

Okay, so now we have this vector in the complex space and we need to first found the country kate, the real part, imaginary part and then the norm of this vector. So they congregate. We only need to change the sign of those numbers that for the imaginary part of the factory, In this case we have six that remained the same one. And here we change it to -4. I. And the last component will be six plus two. I. Okay, so that's the country gate. Then the real part will be the terms that uh doesn't um have the imaginary number the eye. So those that are just the numbers in this case six, 16 And the imaginary parts, those that are multiplied by I. So in this case is 0 -4 and two. The last thing that we need to do is calculate the norm. So in this case is equal to the square root of the dot product of you with its congregate. Okay, these results into the square roots of through six plus one. Last 16 han Plus 36 plus four. This result into the square root of 93.

Were given to factors. You is equal to two I plus J Mom, we can convert this into a component form which would just be too I or +21 and the same thing with V. So v turns into three negative to just looking at the coefficients of each, um I and J. So now we can find the magnitude of you. The magnitude of you is equal to the square root of the sum of the squares of the components is the square root of five and in with scurvy or with magnitude V, we have three squared plus two squared negative two square, which is same thing as tooth positive screwed 24 plus nine is this 13 c squared 13 is our vector or is our magnitude V and for two times you two times you we have four to. So we now do foursquare close to square. This gives us 20 square to 20 just equals who to root five. Or you can believe it as the 20 square twenties find as well. And what half of the is through is uh yeah, 1.5 negative one and the magnitude of these values, plus negative. One squared someone Half a magnitude is square root of one slurred of 13/4 and then we can look at you plus fee. So you plus fee is manager you for we get five negative one and ah, magnitude is five squared. Plus Make it if one squared just 26. So square root of 26 is our magnitude for U plus V and for humanise fee you have native one and three, which means that our, um we now have made it one squared skirt of negative one squared plus three squared, which is 10 square root of 10. And lastly for you manage to the view Money's limited view. What we already know what you issues Screwed of five and magnitude of e is square root of 13 and this is equal to square of 10. You're plugging this into a calculator