Dividing/Multiplying Imaginary Numbers

[cstoos]

Is there a more convenient way to multiply and divide imaginary numbers than converting back and forth from phasors? (I guess I should say "when also having to add and subtract them")

I always find AC circuit calculations to be tedious and problem filled when I do it that way.

For example if I had to simplify something like:



(6+j3)/(6+j8)+(5+j9)/(2+j7)

 

[Hurkyl]

Have you tried rationalizing the denominator? (I suppose "rationalize" is the wrong word here, but it's the same procedure)

 

[cstoos]

I think you are referring to multiplying by the complex conjugate...correct? A possibility yet still tedious when dealing with say, three impedences in parallel.

There is no way to directly divide? Seems like there should be.

Oh, and the above problem is completely made up, so no, I haven't tried that. I was just using it as a visual referrence as to what I was talking about.

 

[Mark44]

There are only two ways that I know about for dividing complex numbers. One way involves the complex conjugate for complex numbers in Cartesian form. The other way is to divide the magnitudes and subtract the arguments (angles) for complex numbers in polar form.

 

[HallsofIvy]

There are only two ways that I know about for dividing complex numbers. One way involves the complex conjugate for complex numbers in Cartesian form. The other way is to divide the magnitudes and subtract the arguments (angles) for complex numbers in polar form.

I believe the "polar form" is what cstoos is referring to as "phasors".

 

[The Chaz]

Is there a more convenient way to multiply and divide imaginary numbers than converting back and forth from phasors? (I guess I should say "when also having to add and subtract them")...
(6+j3)/(6+j8)+(5+j9)/(2+j7)

Well, yes, there is technology!
On the TI-83+ (in a+ bi mode)
...
(6+3i)/(6+8i) + (5+9i)/(2+7i) (MATH-> FRAC)
=
524/265 - (329/530)i.

 

[cstoos]

You and your fancy calculators...

And yes, HallsofIvy is correct in his statement. Polar form is the same a phasors.

For example 6+3i would be written 6.7/26.6


Well, I guess my question was answered. No simpler way to do it. Now one of you just needs to find a new operation that will make my life easier.