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Math Help - differentiation and complex numbers

  1. #1
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    differentiation and complex numbers

    okay just 2 quick ones

    differentiate w = 6t^(-3/2) - 4t^(3/2)

    and given that z = 1 + j and w = 2-3j find

    w/z

    these are the last 2 questions im stuck with and any help would be wicked cheers!.
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  2. #2
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    Quote Originally Posted by mxmadman_44 View Post
    okay just 2 quick ones

    differentiate w = 6t^(-3/2) - 4t^(3/2)

    and given that z = 1 + j and w = 2-3j find

    w/z

    these are the last 2 questions im stuck with and any help would be wicked cheers!.
    What is that supposed to mean?

    You need to be more precise about what w is. And what you mean by w/z.
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  3. #3
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    Quote Originally Posted by mxmadman_44 View Post
    given that z = 1 + j and w = 2-3j find w/z
    This complex division: \frac{w}{z} = \frac{{w\overline z }}{{\left| z \right|^2 }}
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  4. #4
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    complex number

    yes its a complex number division the equation i have is wz*/|z|^2
    im not sure what the star means. should i ignore this?

    any help on the differentiation would be great im not sure what to do with the negative fraction powers
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  5. #5
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    Quote Originally Posted by mxmadman_44 View Post
    differentiate w = 6t^(-3/2) - 4t^(3/2)
    You do it just like any other derivative:
    w^{\prime} = 6 \cdot \left ( -\frac{3}{2} \right )t^{-5/2} - 4 \cdot \left ( \frac{3}{2} \right ) t^{1/2}

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mxmadman_44 View Post
    and given that z = 1 + j and w = 2-3j find

    w/z
    Quote Originally Posted by mxmadman_44 View Post
    yes its a complex number division the equation i have is wz*/|z|^2
    im not sure what the star means. should i ignore this?
    Owwwwch!

    The star means to take the complex conjugate of the variable. So since z = 1 + j, z^* = 1 - j.

    Here it is in its full glory:
    \frac{w}{z} = \frac{2 - 3j}{1 + j}

    The problem with leaving the expression like this is that there is a radical in the denominator, j = \sqrt{-1}, which is typically removed. So if you multiply the denominator by the conjugate of the denominator (in this case rechristened as the "complex conjugate") we get:
    \frac{w}{z} = \frac{2 - 3j}{1 + j}

    = \frac{2 - 3j}{1 + j} \cdot \frac{1 - j}{1 - j} = \frac{(2 - 3j)(1 - j)}{1^2 - j^2}

    = \frac{2 - 2j - 3j + 3j^2}{1 - (-1)} = \frac{2 - 5j + 3(-1)}{1 + 1}

    = \frac{-1 - 5j}{2}

    -Dan
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  7. #7
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    Star? What Star?
    The conjugate of z is {\overline z }.
    Does that appear as z* in your browser? If so, what is the browser?
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  8. #8
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    star

    Quote Originally Posted by Plato View Post
    Star? What Star?
    The conjugate of z is {\overline z }.
    Does that appear as z* in your browser? If so, what is the browser?
    No i am using explorer but on the formulae sheet it is an star not an overline. I think they mean the same thing.
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  9. #9
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    Quote Originally Posted by mxmadman_44 View Post
    No i am using explorer but on the formulae sheet it is an star not an overline. I think they mean the same thing.
    I do know that Europeans often use j in the same way that north American use i. (I did study a year at the University of Manchester UK) but I did not know about using * for conjugate. So yes you are correct about that.
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Plato View Post
    I do know that Europeans often use j in the same way that north American use i. (I did study a year at the University of Manchester UK) but I did not know about using * for conjugate. So yes you are correct about that.
    The asterisk (what you are calling a star) is commonly used in wave mechanics in Physics.

    -Dan
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  11. #11
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    Quote Originally Posted by Plato View Post
    I do know that Europeans often use j in the same way that north American use i. (I did study a year at the University of Manchester UK) but I did not know about using * for conjugate. So yes you are correct about that.
    1. European mathematicians use i exclusively for the imaginary unit. Engineers
    of the electrical/electronic persuasion use j for the imaginary unit to avoid
    confusion with the use of i for current (I had to go through the last paper I
    sent for publication changing all the i's to j's as it was going to a
    nominally electronic engineering journal, though as most of the stuff
    published in it is related to DSP I think they are living in the past).

    2. Often * is used to denote complex conjugate plain in ASCII maths.

    RonL
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