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Math Help - Resources for complex numbers

  1. #1
    Senior Member Mukilab's Avatar
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    Resources for complex numbers

    Hello, Cyf here.

    I'm attempting to learn about complex numbers and I was wondering if anyone had any resources? I've gotten as far a complx conjugates because I have no idea what they are and I've also been given this diagram which I don't understand. Could anyone explain it to me and explain what is arg(z)?

    I don't differentiate between books or sites, as long as either are clear, simple and for the amateur (self-studying, never done this before)

    Any help greatly appreciated.

    ~Cyf

    Edit: I forgot to ask, what does a triple dash mean? Like an equals sign but with one more hyphon in it.

    Edit: Sorry for forgetting the diagram. Here it is:

    Last edited by Mukilab; June 12th 2010 at 09:48 AM.
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  2. #2
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    Complex conjugates

    a + ib and a - ib are complex conjugates (their product is a^2 + b^2) where a and b are real numbers.

    A triple dash means identical.
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  3. #3
    Senior Member Mukilab's Avatar
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    I understand how it means congruent/identical in geometrical shapes but not in algebra

    For complex conjugates I was referring to circumstances such as z*
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  4. #4
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    A good website

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  5. #5
    Senior Member Mukilab's Avatar
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    what is meant by a commer (apologies for the mutation of a language if this is spelt incorrectly) between two values?
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  6. #6
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    It depends

    Quote Originally Posted by Mukilab View Post
    what is meant by a commer (apologies for the mutation of a language if this is spelt incorrectly) between two values?
    I believe you mean either a comma or an apostrophe (need more context or an example).
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  7. #7
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by wonderboy1953 View Post
    I believe you mean either a comma or an apostrophe (need more context or an example).
    comma

    u,v
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  8. #8
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    Depends on the values

    Quote Originally Posted by Mukilab View Post
    comma

    u,v
    For example the comma in 238,231 means the number is over 238 thousand (the comma is being used to make it easier to understand the number).

    Do you have something else in mind when you say values?
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  9. #9
    Senior Member Mukilab's Avatar
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    " Let l = (u, v) be a complex number,"
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  10. #10
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    Answer

    Quote Originally Posted by Mukilab View Post
    " Let l = (u, v) be a complex number,"
    u + iv = 1 is what the comma means in this instance.
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  11. #11
    Senior Member Mukilab's Avatar
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    Why is it written in the form (u,v)?
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  12. #12
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    Probably because

    Quote Originally Posted by Mukilab View Post
    Why is it written in the form (u,v)?
    It's an abbreviation since the i is well understood; also it helps out in complex coordinate geometry (with Argand diagrams).
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  13. #13
    Senior Member Mukilab's Avatar
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    will something such as (a,b) always be a+ib or could it be ia+b or even a-ib?
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  14. #14
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    Answer

    a - ib is the complex conjugate to a + ib so the answer is no there, the other expression ia + b is also regarded as being different since a precedes b (another way of saying this is that order matters).
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