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    Let

     \frac{1}{Z} = \frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3}

    where

     Z_1 = 1

    and

     Z_2 = i\omega

    and

     Z_3 = \frac{1}{i\omega}

    and

     \omega is a real number. Find the real and imaginary parts of Z in terms of  \omega .

    I'd like some help/advice on how to tackle this problem please. Many thanks in advance!
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    write 1/Z = 1 +i(w -1/w)

    then 1/(1 +i(w -1/w)) = Z

    can you carry on from here?
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    (Original post by dark_lord90)
    Let

     \frac{1}{Z} = \frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3}

    where

     Z_1 = 1

    and

     Z_2 = i\omega

    and

     Z_3 = \frac{1}{i\omega}

    and

     \omega is a real number. Find the real and imaginary parts of Z in terms of  \omega .

    I'd like some help/advice on how to tackle this problem please. Many thanks in advance!
    There are various ways. It is hard to tell you how to proceed without knowing what level of maths you have.

    A method you should understand is to make a single fraction for \frac{1}{z}, find the reciprocal and rationalise the denominator (multiply by the conjugate).

    The substitution t=w-\frac{1}{w} may make it easier for you to see what is going on.
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    (Original post by geo3)
    how do you do this?(using a simple method)
    Use \displaystyle \frac{1}{a+ib} = \frac{1}{a+ib} \times \frac{a-ib}{a-ib} = \frac{a-ib}{a^2+b^2}
 
 
 
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Updated: November 16, 2008
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