SOLUTION: Given the equivalent impedance of a circuit can be calculated by the expression Z=(Z1*Z2)/(Z1+Z2) If Z1 = 1+j5 and Z2 = 12+j3, calculate the impedance Z in both rectangular a

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Given the equivalent impedance of a circuit can be calculated by the expression Z=(Z1*Z2)/(Z1+Z2) If Z1 = 1+j5 and Z2 = 12+j3, calculate the impedance Z in both rectangular a      Log On


   



Question 1062350: Given the equivalent impedance of a circuit can be calculated by the expression
Z=(Z1*Z2)/(Z1+Z2)
If Z1 = 1+j5 and Z2 = 12+j3, calculate the impedance Z in both rectangular and polar forms

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+Z+=+Z1%2AZ2%2F+%28Z1%2BZ2%29+ =
+%281%2Bj5%29%2812%2Bj3%29+%2F+%281%2Bj5%2B12%2Bj3%29+ =
+%2812%2Bj3%2Bj60%2Bj%5E2%2815%29%29+%2F+%2813%2Bj8%29+ =
+%28-3%2Bj63%29%2F%2813%2Bj8%29+ =
+%28-3%2Bj63%29%2A%2813-j8%29+%2F+%28%2813%2Bj8%29%2A%2813-j8%29%29+ =
+%28-39%2Bj24%2Bj819-j%5E2%28504%29%29+%2F+%28169-j%5E2%2864%29%29+ =
++%28465%2Bj843%29+%2F+%28233%29+ (rectangular form with integers) =
++Z+=+1.9957+%2B+j3.618+ (rectangular form)

Polar form: +r=sqrt%281.9957%5E2%2B3.618%5E2%29+=+4.1319+
+theta+=+arccos%281.9957%2F4.1319%29+=+61.12%5Eo+
+Z+=+4.1319+ /_ +61.12%5Eo+ (polar form, where /_ means "at angle")


For reference Z = r/_theta = r*e^(j*theta) = r*(cos (theta) + j*sin (theta))