18 divide (2 - 4i)/(3 - 2i)

Answer:

$\frac{14}{13}-\frac{8}{13}i$

Explanation:

Step1: Multiply numerator and denominator by the conjugate

Multiply (\frac{2 - 4i}{3 - 2i}) by (\frac{3 + 2i}{3 + 2i}) [ \frac{(2 - 4i)(3 + 2i)}{(3 - 2i)(3 + 2i)} ]

Step2: Expand the numerator and denominator

Use the FOIL method for the numerator: ((2\times3)+(2\times2i)+(-4i\times3)+(-4i\times2i)=6 + 4i-12i - 8i^{2}) Since (i^{2}=-1), the numerator becomes (6-8i + 8=14-8i) For the denominator: ((3\times3)+(3\times2i)+(-2i\times3)+(-2i\times2i)=9+6i - 6i-4i^{2}) Since (i^{2}=-1), the denominator becomes (9 + 4=13)

Step3: Write the result

[ \frac{14-8i}{13}=\frac{14}{13}-\frac{8}{13}i ]