The correct answer is [tex]\frac{4}{3-2i}=\frac{12}{13}+i\frac{8}{13}[/tex]
Steps:
[tex]\mathrm{Multiply\:by\:the\:conjugate}\:\frac{3+2i}{3+2i}, =\frac{4\left(3+2i\right)}{\left(3-2i\right)\left(3+2i\right)}[/tex]
[tex]\left(3-2i\right)\left(3+2i\right)=13, =\frac{4\left(3+2i\right)}{13}[/tex]
[tex]\mathrm{Rewrite\:}\frac{4\left(3+2i\right)}{13}\mathrm{\:in\:standard\:complex\:form:\:}\frac{12}{13}+\frac{8}{13}i[/tex]
[tex]=\frac{12}{13}+\frac{8}{13}i[/tex]
