Question about adding complex numbers

[CE Trainee]

Homework Statement

I was working on a problem dealing with complex numbers. I had to add two phasors together to get the combined phasor. I converted both numbers to rectangular form, added them and converted the result back to polar form. My magnitude was correct, but my phase was not.

Homework Equations

rectangular form of both complex numbers added together: -1.204 + j0.9476.

magnitude : 1.532.

phase: -38.2043 degrees

book answer: 1.532e^j141.79

The Attempt at a Solution

I don't really understand why I didn't get the phase right. I took the arctan of y / x and got the wrong answer. Just for the heck of it, I decided to randomly add 180 to my phase and got 141.79. What effect did this have? Why did I need to add 180? How was I supposed to know I needed to add 180?

Thanks

 

[Dick]

tan(141.79) and tan(-38.2043) both give you the same y/x. The tip off is that the polar form of 141.79 will be in the second quadrant (negative x and positive y). The polar form of -38.2043 is in the fourth quadrant (positive x and negative y). arctan can't tell the difference. You can if you look at the original number. You want the second quadrant one.

 

[yungman]

Homework Statement

I was working on a problem dealing with complex numbers. I had to add two phasors together to get the combined phasor. I converted both numbers to rectangular form, added them and converted the result back to polar form. My magnitude was correct, but my phase was not.

Homework Equations

rectangular form of both complex numbers added together: -1.204 + j0.9476.

magnitude : 1.532.

phase: -38.2043 degrees

book answer: 1.532e^j141.79

The Attempt at a Solution

I don't really understand why I didn't get the phase right. I took the arctan of y / x and got the wrong answer. Just for the heck of it, I decided to randomly add 180 to my phase and got 141.79. What effect did this have? Why did I need to add 180? How was I supposed to know I needed to add 180?

Thanks

rectangular form of both complex numbers added together: -1.204 + j0.9476.

tell you that it is r=-ve this give the phasor in the second quadrant.

your -38.2043 is from -ve r-axis to the phasor. The angle from +ve r-axis is 180-38.2043=141.79. Which is the same as the answer.

 

[CE Trainee]

tan(141.79) and tan(-38.2043) both give you the same y/x. The tip off is that the polar form of 141.79 will be in the second quadrant (negative x and positive y). The polar form of -38.2043 is in the fourth quadrant (positive x and negative y). arctan can't tell the difference. You can if you look at the original number. You want the second quadrant one.

Hmm, that makes sense. The weird thing is, i took arctan manually with my calculator and got -38.2043. However, when I put the entered the number into my calculator as rectangular and let the calculator convert it to polar, it knew to print 141.79.

 

[Dick]

Hmm, that makes sense. The weird thing is, i took arctan manually with my calculator and got -38.2043. However, when I put the entered the number into my calculator as rectangular and let the calculator convert it to polar, it knew to print 141.79.

When you used the polar converter it knew x was positive and y was negative. If you just put in y/x there is no way to tell the signs of x or y.