Question

Simplify the given answer


`(4)/(3 - 2i)`
a. 4/13
b. 16/13
c. (12+8i)/13
d. (12-8i)/13

Answer 1

`(4)/(3 - 2i) \\ \\ = (4)/(3 - 2i) * (3 + 2i)/(3 + 2i) \\ \\ = (4 * (3 + 2i))/((3 - 2i)(3 + 2i)) \\ \\ = \frac{4(3 + 2i)}{ {3}^(2) - {(2i)}^(2) } \\ \\ = (12 + 8i)/(9 + 4) \\ \\ = \boxed{(12 + 8i)/(13) } \\ \\`

`\boxed{\textbf{\huge{\red{Answer : C}}} }`