Answer:
[tex]\frac{4}{13}-\frac{7}{13}i[/tex]
Step-by-step explanation:
[tex]\frac{2-i}{3+2i}[/tex]
Multiply and divide by the conjugate.
The conjugate is the denominator with the sign of the complex number the opposite of the denominator.
[tex]\frac{2-i}{3+2i}\frac{3-2i}{3-2i}\\ =\frac{2\times (3-2i)-i\times (3-2i)}{3^2-(2i)^2}\\ =\frac{6-4i-3i+2i^2}{9+4}\\ =\frac{4-7i}{13}\\ =\frac{4}{13}-\frac{7}{13}i[/tex]
Quotient = [tex]\frac{4}{13}-\frac{7}{13}i[/tex]
