jmc

Question

Complex numbers are often used when dealing with alternating current (AC) circuits. In the equation V = IZ, V is voltage, I is current, and Z is a value known as impedance. If V = 1+i and Z=2-i, find I.

Accepted Answer

We have I = VZ = 1+i2-i. Multiplying the numerator and denominator by the conjugate of the denominator, we get I = 1+i2-i 2+i2+i = 1(2) + 1(i) + i(2) + i(i)2(2) + 2(i) - i(2) - i(i) = 1+3i5 = 15 + 35i .