Complex number are used to describe current I voltage E and

Complex number are used to describe current, I voltage, E and impedance Z These three quantities are related by the equation E = 12 Given two of these quantities solve the equation E = 1z for the missing (simplify your answer. Type you answer a + bi. Use integers or fraction for any numbers in the expression.)

Solution

E = i*Z

Z = E/i

E = 9 + 8i

i = 9 + 4i

So,

Z = (9 + 8i)/(9 + 4i)

Z = [(9 + 8i)/(9 + 4i)]*[(9 - 4i)/(9 - 4i)]

Z = (9 + 8i)*(9 - 4i)/[(9 + 4i)*(9 - 4i)]

Z = (81 - 32*i^2 + 36 i)/(81 - 16*i^2)

i^2 = -1

Z = (113 + 36 i)/(81 + 16)

Z = 113/97 + i*(36/97)

Z = 1.165 + 0.371 i