- #1
LDC1972
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Homework Statement
Given the equivalent impedance of a circuit can be calculated by the expression:
Z = Z1 X Z2 / Z1 + Z2
If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form.
Homework Equations
Multiplication and division of complex numbers.
The Attempt at a Solution
I want to solve the rectangular first. As I want to totally understand how this is done. My attempt so far:
Z1 + Z2 = 4 + j10 + 12 + j3
= 4 + 12 + J10 - J3
Z1 + Z2 = 16 + j7
Z1 x Z2 = 4 + j10 x 12 - j3
= (4 x 12) + (12 x j10) + (4 x -j3) + (j10 x j3)
= 48 + j120 - j12 - j^2 30
Since j^2 = -1
Then
Z1 x Z2 = 48 + j108 - (-1) 30
= 48 + j108 +30
Z1 x Z2 = 78 + j108
Z = 78 + j108 multiply by conjugate 16 - j7
----------- -------
16 + j7 16 - j7
Z = -1248 - j1728 - j546 - j^2 756
----------------------------------
16^2 + 7^2
-1248 - 756 = 2004
j1728 - j546 = j1182
Z = -2004 - j1182
---------------
305
-2004 / 305 = -6.570491803
j1182 / 305 = 3.875409836
Z = 6.5705 ± j3.8754