### Instruction: 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 $Z=1+3i$, find $I$.  Express your answer as a complex number in the form $a+bi$, where $a$ and $b$ are real numbers.### Response: Ok, so we can use the equation $V=IZ$ to find $I$.
So if we divide both sides of the equation by $Z$, we can find $I$.
Right. So let's divide $V$ by $Z$.
So we have $\frac{1-i}{1+3i}$, which is equal to $\frac{(1-i)(1-3i)}{(1+3i)(1-3i)}$.
And then we have $\frac{1-3i-i+3i^2}{1-3i+3i-9i^2}$.
After we simplify, we get $\frac{1-4i+3i^2}{1-9i^2}$.
Well, $i^2$ is equal to $-1$, so we have $\frac{1-4i+3(-1)}{1-9(-1)}$.
And then we have $\frac{1-4i-3}{1+9}$.
So if we simplify the numerator, we get $-2-4i$.
And if we simplify the denominator, we get $10$.