Mesh Current Method (complex numbers part)

AI Thread Summary
The discussion focuses on understanding the conversion of complex numbers in the mesh current method used in electronics. The key point is the transformation from the rectangular form 4-j7 to polar coordinates, resulting in a magnitude of 8.0623 and an angle of -60.2551 degrees. The magnitude is calculated using the Pythagorean theorem, while the angle is derived from the arctangent of the imaginary component over the real component. The negative angle indicates the direction of the vector in the complex plane, which is essential for proper interpretation in electrical engineering contexts. This conversion is crucial for solving mesh current problems involving complex numbers.
andymarra
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Basically, part of my uni course is electronics and some of the mesh current method questions involve complex numbers, mainly the use of j and other things. I would get the answer as the solution gets it down to 4-j7 and then it says this equals 8.0623<-60.2551° ......... ...< is supposed to be like/_ but couldn't find the proper symbol. I just can't understand the meaning of j and such things. How does it get from 4-j7 to this other answer? Just wondering if anyone could explain the conversions of these symbols to normal numbers and degrees as it is saying the final answer is? can provide full solution if needed.
Thanks, Andy


I can do the question, and understand most of it, its a solution from a past paper in university, but I am having trouble understanding only the complex numbers part, mainly the way in which it changes from j over to a number and degrees? i understand only that j is the sqrt of -1. Any help appreciated! Thanks again! Andy
 
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j is the imaginary component. If you've taken mechanical physics, and I assume you have, you can think of anything with a j as being the "y-component" and anything without it being the "x-component"

http://en.wikipedia.org/wiki/Imaginary_number

Look at that graph. Like I said earlier, the imaginary axis is the y-axis, and the real axis is the x-axis. You can represent any rectangular coordinate as a magnitude and an angle.
 
okay I understand what you're saying, but how does this make 4-j7=8.0623<-60.2551? is there a further calculation that is needed to convert this? Thanks
 
andymarra said:
okay I understand what you're saying, but how does this make 4-j7=8.0623<-60.2551? is there a further calculation that is needed to convert this? Thanks

the magnitude is the squares of the real and the square of the imaginary added and then square rooted:
\sqrt{4^2 + (-7)^2} = 8.0623

the angle is sort of the arctan of the imaginary over the real. Sometimes, you need to modify the angle slightly, because your calculator doesn't know the difference between
arctan[ (-y)/x] and arctan[ y/(-x)]
arctan(\frac{-7}{4}) = -60.2551^o

so the final answer is
8.0623 \angle -60.2551^o=8.0623e^{-1.0517j}
 
andymarra said:
okay I understand what you're saying, but how does this make 4-j7=8.0623<-60.2551? is there a further calculation that is needed to convert this? Thanks

You convert from rectangular to polar coordinates.

The horizontal (real) component is 4, so that is a vector that points to the right along the x axis. The vertical (imaginary) component is -7, so that is a vector that points down. Adding the two vectors gives you the complex result, which is a vector that starts at the origin, and points down to the right. Its length is the hypotenuse of the right triangle (base = 4, height = 7 down), and the angle it forms with the positive x-axis is -60 degrees. The convention for that angle in the rectangular-to-polar conversion is that the angle is positive starting at the x-axis and going in the counter-clockwise direction. So going in the opposite direction makes the angle negative by convention.

Does that make sense?


EDIT -- Ack, beat out again by xcvxcvvc!
 

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