contestada

simplify the given answer
[tex] \frac{4}{3 - 2i} [/tex]
a. 4/13
b. 16/13
c. (12+8i)/13
d. (12-8i)/13

Respuesta :

TPS00

[tex] \frac{4}{3 - 2i} \\ \\ = \frac{4}{3 - 2i} \times \frac{3 + 2i}{3 + 2i} \\ \\ = \frac{4 \times (3 + 2i)}{(3 - 2i)(3 + 2i)} \\ \\ = \frac{4(3 + 2i)}{ {3}^{2} - {(2i)}^{2} } \\ \\ = \frac{12 + 8i}{9 + 4} \\ \\ = \boxed{\frac{12 + 8i}{13} } \\ \\ [/tex]
[tex] \boxed{\textbf{\huge{\red{Answer : C}}} }[/tex]

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