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I'm looking for someone validation. I am an engineering student doing calculations on power although I'm pretty sure its irrelevant.

Now from my mathematics high school days I always remember that when multiplying complex numbers you multiply the magnitude and add the angles and when doing division you divide the magnitudes and subtract the angles.

I am preparing for a national exam. We have been given previous past papers to help that come with the official answer sheets that were used in the previous national examinations and I'm staring at what seems impossible.

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There are 3 sets of calculations. One for AB, BC and CA.

The first AB seems correct in that the angles have been added yet BC and CA the angles seem to have been subtracted. Am I missing something here? Is there something advanced about complex numbers and multiplication I don't know?

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    $\begingroup$ No, there's nothing advanced about complex numbers that would hinder the calculation. It seems awfully likely that the negative sign on the 120 in the second problem ought to have been on the 120 in the third problem. $\endgroup$
    – rschwieb
    May 9, 2017 at 18:59
  • $\begingroup$ Actually the angles are right they are differences of phase at 0, -120 and 120 respectively. The actual original numbers are correct its just the final answers as I suspected are wrong. $\endgroup$
    – Ryan Walkowski
    May 9, 2017 at 19:02
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    $\begingroup$ Well, in all three cases it looks like the first angle is being subtracted from the second angle. If that is really what should be happening here, then it has to do with the physics of the computation, not the mathematics. TBH this piece of paper is covered with an unreadable soup of symbols bearing little resemblence to complex multiplication, to me. $\endgroup$
    – rschwieb
    May 9, 2017 at 19:03
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    $\begingroup$ If the correct procedure is to multiply the polar forms as written, then I think your conclusion that the answers are incorrect is the right one. $\endgroup$
    – rschwieb
    May 9, 2017 at 19:04
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    $\begingroup$ These engineering papers always seem to deviate from standard symbols its actually annoying when you are trying to independently research it as it never corresponds to what's out there. But I'm glad its not just me that thinks it looks wrong. $\endgroup$
    – Ryan Walkowski
    May 9, 2017 at 19:06

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