Math Is Fun Forum

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

factoring i and complex expressions

how do u factor complex numbers??? is there any way to do taht???
like (4+3i)(6+2i) = 18 +26i
but how do we get from 18 +26i back to (4+3i)(6+2i)???

ive gotten this far.

x+yi = (a+bi)(c+di)
x+yi = ac + adi + bci - bd
x = ac - bd
yi = adi + bci
y = ad + bc

so can anyone help with this???

also is there some type of property or theroem or law or relations ship or something b/w

ad + bc

and

ac - bd

that i dont no about or something??

i no there could be many possible answers when factoring complex numbers but how do u get at least one of them?

Last edited by shocamefromebay (2007-06-05 02:21:41)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: factoring i and complex expressions

Possibly slightly off-topic, but (1+2i)(6+3i) = 15i.

Anyway, you've already found out what the problem basically is.
You've reduced it to two simultaneous equations (although the first should have -bd instead of +bd), and so to factorise the complex numbers you just need to solve those.

ac - bd = x
ad + bc = y

There are two equations and four variables, which means that two of those variables are free.
You can pick any two and fix them to be some value, which will then let you solve for the other two (with a few exceptions).

For example, if you wanted to factorise it so that the real parts of both factors was one, then you would get 1 - bd = x; d + b = y.

Or if you wanted the factors to be the same, then you would set a=c, b=d and be left with
a²-b² = x, 2ab = y.

The one thing you do need to be careful of is if you set free variables to equal 0.
If you do that, then one of the two equations might become inconsistent. For example, setting c=d=0 would turn the second equation into 0a + 0b = y, which clearly has no solution for non-zero values of y. Other than that though, you're free to do whatever you want and a solution should always be there.

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Why did the vector cross the road?
It wanted to be normal.

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Re: factoring i and complex expressions

is there any way to make sure taht all of the variables are interegers?
and can u give me an example of what u mean or are trying to say?

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: factoring i and complex expressions

The solution for two complex numbers to multiply to a given one is Not Only. They are a lot. Think of one pair, then I multiply one of it by a complex factor, and divide the other by the same factor, woo! another solution pair!!

So after some analysis, the only way to get your convenient solution (ideally integer coefficients) is to guess.

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X'(y-Xβ)=0

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Re: factoring i and complex expressions

well ive really not learned how to factor i expressions here
but what i did learn is how to divide complex numbers!
which is just as good
w00t

malygia

Member

Registered: 2007-06-12

Posts: 1

Re: factoring i and complex expressions

If 2.53% of ? = $2.32 what is ?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: factoring i and complex expressions

You should really post new questions in a new topic, rather than piggybacking someone else's.

Still, it seems like the original question has been answered so it doesn't matter too much this time.

2.53% of ? is equivalent to saying (2.53x?)/100.
Therefore, (2.53x?)/100 = $2.32

2.53x? = $232
? = $232/2.53 = $91.70 (to nearest cent)

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Why did the vector cross the road?
It wanted to be normal.

malygia

Member

Registered: 2007-06-12

Posts: 1

Re: factoring i and complex expressions

If 2.53% of X = $2.32 what is X

Can someone please tell me how to solve this problem.
Im sure this is a very simple problem for most of you
math heads out there, but as much as I like math,
I am not very good at it. As you can tell by my question.
I dont even know if I have layed it out correctly.
Probably not.

Last edited by malygia (2007-06-14 15:15:45)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: factoring i and complex expressions

mathsyperson just solved it (read above)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman