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Math Help - Don't understand how to do this please help

  1. #1
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    Don't understand how to do this please help

    the impedance of a circuit can be calculated by the expression

    Z = Z1 X Z2 / Z1 + Z2

    If Z1 = 4 + j10 & Z2 = 12 - j3

    how do I calculate the impedance Z in rectangular and polar forms?
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  2. #2
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    Re: Don't understand how to do this please help

    First, we need to know what the formula really is. Is it
    Z= (Z1)\left(\frac{Z2}{Z1}\right)+ Z2
    which is what you wrote, or is it
    Z= \frac{Z1Z2}{Z_1+ Z_2}?

    With Z1= 4+ j10, Z2= 12- j3, Z1+ Z2= 16+ j7. Now, write the three numbers, 4+j10, 12- j3, and 16+ j7 in polar form: for 4+ j10, r= \sqrt{4^2+ 10^2}= \sqrt{116} and [itex]\theta= arctan(10/4)= arctan(5/2)= 1.19.

    Multiplying r_1 cis(\theta_1)= r_1e^{i\theta_1} and r_2 cis(\theta_2)= r_2e^{i\theta_2} gives (r_1r_2) cis(\theta_1+ \theta_2)= (r_1r_2)e^{i(\theta_1+ \theta_2)}
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  3. #3
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    Re: Don't understand how to do this please help

    sorry its

    Z = (Z1 x Z2) / (Z1 + Z2)
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  4. #4
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    Re: Don't understand how to do this please help

    sorry kinda lost me from here on, see below, can you explain more

    [itex]\theta= arctan(10/4)= arctan(5/2)= 1.19
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