# Dividing/Multiplying Imaginary Numbers

1. May 17, 2010

### 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)

2. May 17, 2010

### Hurkyl

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

3. May 17, 2010

### 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.

4. May 17, 2010

### Staff: Mentor

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.

5. May 18, 2010

### HallsofIvy

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

6. May 18, 2010

### The Chaz

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.

7. May 18, 2010