SOLUTION: Corrosion in the metal surface of an airplane can be difficult to detect visually. One test used to locate it involves passing an alternating current through a small area on the pl

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Question 560058: Corrosion in the metal surface of an airplane can be difficult to detect visually. One test used to locate it involves passing an alternating current through a small area on the plane’s surface. If the current varies from one region to another, it may indicate that corrosion is occurring. The impedance Z (or opposition to the flow of electricity) of the metal is related to the voltage V and current I by the equation, where Z, V, and I are complex numbers.
Calculate Z for the given values of V and I.
V=10+20i I=3+7i
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The impedance Z (or opposition to the flow of electricity) of the metal is related to the voltage V and current I by the equation, where Z, V, and I are complex numbers.
Calculate Z for the given values of V and I.
V=10+20i I=3+7i
:
Z = V/I
:
Z = %28%2810%2B20i%29%29%2F%28%283%2B7i%29%29
:
multiply by the conjugate of the denominator over itself
Z = %28%2810%2B20i%29%29%2F%28%283%2B7i%29%29 * %28%283-7i%29%29%2F%28%283-7i%29%29 = %2830-70i%2B60i-140%28i%5E2%29%29%2F%289-49%28i%5E2%29%29 = %2830-10i-140%28-1%29%29%2F%289-49%28-1%29%29 = %2830-10i%2B140%29%2F%289%2B49%29 = %28170-10i%29%2F%2858%29