### Instruction: Simplify $\displaystyle\frac{1-i}{2+3i}$, where $i^2 = -1.$.### Response: To simplify a complex fraction like this, I need to multiply the numerator and denominator by the conjugate of the denominator, which is $2-3i.$
This will make the denominator a real number, and then I can simplify the numerator by using the distributive property and the fact that $i^2 = -1.$