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 $I$.

Answer 1

I = V/Z = (1 + i)/(2 - i). Multiply numerator and denominator by the conjugate of the denominator (2 + i):

I = (1 + i)(2 + i) / [(2 - i)(2 + i)] = (1 + 3i) / 5 = 1/5 + (3/5)i.

So I = 0.2 + 0.6 i.