1. If I want to find some actual meaning from an equation containing complex numbers, can I do this:

x(t) = (4 + 3i)*(exp(-2t) - exp(5it))

Re[x(t)] = Re[4 + 3i] * ( exp(-2t) - Re[exp(5it)] )

where I just take the real portion of each complex number, and drop the imaginary parts?

I feel like I'm missing something - someone let me know. Thanks!  2.

3. Originally Posted by ConiunctoErgoSum
If I want to find some actual meaning from an equation containing complex numbers, can I do this:

x(t) = (4 + 3i)*(exp(-2t) - exp(5it))

Re[x(t)] = Re[4 + 3i] * ( exp(-2t) - Re[exp(5it)] )

where I just take the real portion of each complex number, and drop the imaginary parts?

I feel like I'm missing something - someone let me know. Thanks!
Yep you are missing quite a bit. The real part of a product is not the product of the real parts.  4. so... what, then, is the real part of a product?  5. Originally Posted by ConiunctoErgoSum
so... what, then, is the real part of a product?
Work it out for yourself. It is extremely easy.  6. Let and . Find .  7. Originally Posted by Ellatha
Let and . Find .
You have the right idea.

But your notation suggests two functions f and g of some variable x. There is no "x" on the right side of the "=" sign, nor is one needed.

All one needs to do is work out Re(a+bi)(c+di) vs ac.  8. Originally Posted by DrRocket Originally Posted by Ellatha
Let and . Find .
You have the right idea.

But your notation suggests two functions f and g of some variable x. There is no "x" on the right side of the "=" sign, nor is one needed.

All one needs to do is work out Re(a+bi)(c+di) vs ac.
I agree that the notation I used was rather sloppy. If one prefers, it could be viewed as and . Constant functions, i.e., are similar.

I also agree that the answer to this question is extremelly simple:  Now let and . Therefore, multiplying the binomials derives the binomial , where is the real part and C is the real coefficient of the imaginary number .  Bookmarks
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