SOLUTION: Given the equivalent impedance of a circuit can be calculated by the expression 𝑍=𝑍1𝑍2/𝑍1+𝑍2 If 𝑍1=5𝑗−10 and 𝑍2=6𝑗−8 , calculate the impedance

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Given the equivalent impedance of a circuit can be calculated by the expression 𝑍=𝑍1𝑍2/𝑍1+𝑍2 If 𝑍1=5𝑗−10 and 𝑍2=6𝑗−8 , calculate the impedance       Log On


   

Question 1206628: Given the equivalent impedance of a circuit can be calculated by the expression
𝑍=𝑍1𝑍2/𝑍1+𝑍2
If 𝑍1=5𝑗−10
and 𝑍2=6𝑗−8
, calculate the impedance 𝑍 in polar and rectangular form
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Just in rectangular coordinants:

We math people's "i" is you EE people's "j".

Z=%28Z%5B1%5DZ%5B2%5D%29%2F%28Z%5B1%5D%2BZ%5B2%5D%29
matrix%281%2C2%2Cif%2C+Z%5B1%5D=5j-10%29
matrix%281%2C2%2Cif%2C+Z%5B2%5D=6j-8%29


Z=%28+%285j-10%29%286j-8%29+%29%2F%28+%285j-10%29%2B%286j-8%29+%29

Z=+%2830j%5E2-40j-60j%2B80+%29%2F%285j-10%2B6j-8%5E%22%22+%29

Since j2 = -1

Z=+%2830j%5E2-100j%2B80+%29%2F%2811j-18%5E%22%22+%29 

Z=+%2830%28-1%29-100j%2B80+%29%2F%2811j-18%5E%22%22+%29 

Z=+%28-30-100j%2B80+%29%2F%2811j-18%5E%22%22+%29

Z=+%28-100j%2B50%29%2F%2811j-18%29

Z=+%28%28-100j%2B50%29%2F%2811j-18%29%29%28expr%28%2811j%2B18%29%2F%2811j%2B18%29%29%29

Z=+%28-1100j%5E2-1800j%2B550j%2B900%29%2F%28121j%5E2-324%29

Z=+%28-1100%28-1%29-1855j%2B900%29%2F%28121%28-1%29-324%29

Z=+%281100-1250j%2B900%29%2F%28-445%29

Z=+%28-1250j%2B2000%29%2F%28-445%29

Divide top and bottom by -5:

Z=+%28250j-400%29%2F89

Z=expr%28250%2F89%29j-400%2F89

Z=2.809j-4.494

Edwin