Complex number problem?

Question

when multiplying complex number problems, is it best to change the i or -i or i^2 at the very beginning, in the original problem, or at the end when you get the answer?
ex- ( 2 - i^2) * (-3 - i^2)
would i do(2 * -3) + (2 * -i^2) + (-i^2 * -3) + (-i^2 * -i^2)
-6 + -2i^2 + 3i^2 + i^4

thanks

Answer 1

If there is an i^2 in the problem, I'd change this to a -1 immediately. That saves you a lot of headache in keeping up with i's all over the place.

Answer 2

Personally, I'd go with getting rid of the imaginary terms wherever I could. that way you don't have obnoxious exponents to deal with.

( 2 - i²) * (-3 - i²)
Would become
(2 - -1)*(-3 - -1)=(2+1)(-3+1)
Which would become
3*(-2) = -6

The only time you need to track the imaginary terms is if, after doing the multiplication, or addition, or whatever, you still have a term with a factor of i (√(-1)).
( 2 - i) * (-3 - i)=(2-i)(3) + (2-i)(-i) distributive property

= (2)(3) + (-i)(3) + (2)(-i) + (-i)(-i) distributive property again
= 6 + (-3)i + (-2)i -1
= 5 + (-3-2)i = 5 - 5i
Then you need to keep track of the imaginary terms.

You can pretty much tell when you to worry about them by looking for even and odd exponents. If the exponents on the imaginary terms are even, you can convert them to real numbers. If the exponents are odd, you're stuck with imaginary terms.

Answer 3

It's always easier to simplify things before multiplying. The shorter the factors are, the fewer terms you need to deal with. Since i^2 = -1, both of the factors in your multiplication problem are purely real, and so it's much easier to convert them first:

(2 - i^2) * (-3 - i^2)
= (2 + 1) * (-3 + 1)
= 3 * -2
= -6

Answer 4

i^2 is equal to -1, so your problem really isn't a true complex multiplication (unless you copied it down wrong, or something).

In this case I would convert it first.
(2- -1) * (-3 - -1) = 3*-2 = -6

Your way works, too -- same answer.
.

Answer 5

It's probably personal preference really as it makes to difference to the final answer.

I'd say if you are working with i^2 all the time then it's an automatic thought in your head "yeah, that means -1", but if it's something you do infrequently I'd probably change it straight away so that you don't have to keep doing the conversion in your head. :)

Answer 6

Its math. There are no real rules. Do it however you feel you want to... whatever is more easy for you... whatever you conceptualize better.

Personally, I would simplify what I could... as I could... as I go through the process of solving. Simplicity is always better.

Answer 7

I'm a proffesor, myself.
The answer to that question is -6.