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Math Help - Complex numbers help

  1. #1
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    Complex numbers help

    tt
    Last edited by def77; February 26th 2010 at 02:24 PM.
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  2. #2
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    I am not sure what the question says.
    However, the following is true.
    \frac{1}{z} = \frac{1}{{z_1 }} + \frac{1}<br />
{{z_2 }} + \frac{1}{{z_3 }} \Leftrightarrow \quad \frac{{\overline z }}<br />
{{\left| z \right|^2 }} = \frac{{\overline {z_1 } }}<br />
{{\left| {z_1 } \right|^2 }} + \frac{{\overline {z_2 } }}<br />
{{\left| {z_2 } \right|^2 }} + \frac{{\overline {z_3 } }}<br />
{{\left| {z_3 } \right|^2 }}

    That makes finding the real and imaginary parts easy.
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  3. #3
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    tt
    Last edited by def77; February 26th 2010 at 02:24 PM.
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  4. #4
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    You do know about the conjugate of a complex number don’t you?
    \overline {\left( {x + iy} \right)}  = x - iy

    \left| {iw} \right| = \left| i \right|\left| w \right| = \left| w \right|
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  5. #5
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    Quote Originally Posted by Plato View Post
    You do know about the conjugate of a complex number donít you?
    \overline {\left( {x + iy} \right)} = x - iy

    yep, just doing my numerators, getting -1 - iw - 1/(iw) if i'm assuming x for the conjugate is 0, though i'm a bit iffy on whether the complex conjugate of 1/iw is -1/iw. next for the modulus of iw
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  6. #6
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    Quote Originally Posted by def77 View Post
    yep, just doing my numerators, getting -1 - iw - 1/(iw) if i'm assuming x for the conjugate is 0, though i'm a bit iffy on whether the complex conjugate of 1/iw is -1/iw. next for the modulus of iw
    w = x + iy \Rightarrow \quad \left( {\frac{1}<br />
{{iw}}} \right) = \frac{{\overline {iw} }}<br />
{{\left| w \right|^2 }} = \frac{{ - y - ix}}<br />
{{x^2  + y^2 }}
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  7. #7
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    Quote Originally Posted by Plato View Post
    w = x + iy \Rightarrow \quad \left( {\frac{1}<br />
{{iw}}} \right) = \frac{{\overline {iw} }}<br />
{{\left| w \right|^2 }} = \frac{{ - y - ix}}<br />
{{x^2 + y^2 }}
    great, so if '1/iw' is that, then it can be flipped over to give me 'iw'. what im worrying about is that each of these (x^2 + y^2) are different values, i seem a wee bit out of my depth and i'll ask my professors tommorow see what they think, but i'll troop on for a while, see if i can make some progress on this. thanks for all the help so far, i'm starting to see the problem in context
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  8. #8
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    Quote Originally Posted by def77 View Post
    so if '1/iw' is that, then it can be flipped over to give me 'iw'.
    NO!
    \mbox{Re}(iw) =  - \mbox{Im}(w)\; \;\&\;\; \mbox{Im}(iw)=\mbox{Re}(w)
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  9. #9
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    I thought I understood complex numbers and had a go at this qu but I cannot get a correct answer for the conjugate/ modulus of z3. Does the conjugate of 1/iw = -1/w and the modulus = 1/w ??? I have confused myself and now want to know how to do it!
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