Final answer:
To simplify -2+3i/-3-2i, multiply both the numerator and denominator by the conjugate of the denominator (-3+2i).
Step-by-step explanation:
To simplify -2+3i/-3-2i, we can multiply both the numerator and denominator by the conjugate of the denominator, which is -3+2i. This will help us eliminate the imaginary terms in the denominator.
Multiplying the numerator and denominator, we get:
(-2+3i)(-3+2i) / (-3-2i)(-3+2i)
Expanding and simplifying:
(6i+4i^2-9+6i) / (9+4)
Combining like terms:
(-9+12i+4i^2) / 13
Since i^2 is equal to -1, the expression becomes:
(-9+12i-4) / 13
Combining like terms:
(-13+12i) / 13
Therefore, the simplified form of -2+3i/-3-2i is (-13+12i) / 13.