### 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: To find $I$, I need to divide both sides of the equation by $Z$.
This will give me $I = \frac{V}{Z}$.
However, to simplify the fraction, I want to multiply the numerator and denominator by the complex conjugate of the denominator.
The complex conjugate of $1+3i$ is $1-3i$, which is obtained by changing the sign of the imaginary part.
So, I multiply both the numerator and denominator by $1-3i$, and I get $I = \frac{V}{Z} \cdot \frac{1-3i}{1-3i} = \frac{(1-i)(1-3i)}{(1+3i)(1-3i)}$.
Next, I use the distributive property and the fact that $i^2 = -1$ to expand and simplify the numerator and denominator.
I get $I = \frac{1-3i-i+3i^2}{1-3i+3i-9i^2} = \frac{1-4i-3}{1+9} = \frac{-2-4i}{10}$.