Respuesta :
We are given with a complex no. and need to simplify it , so let's start !!!
Let's assume that :
[tex]{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}}[/tex]
Now , Rationalizing the denominator or in other words multiplying and dividing [tex]{z}[/tex] by the conjugate of the denominator
[tex]{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}\times \dfrac{3+\iota}{3+\iota}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{(6+2\iota)(3+\iota)}{(3-\iota)(3+\iota)}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{6(3+\iota)+2\iota (3+\iota)}{(3)^{2}-(\iota)^{2}}\quad \qquad \{\because (a-b)(a+b)=a^{2}-b^{2}\}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{18+6\iota +6\iota +2(\iota)^{2}}{9-(-1)}\quad \qquad \{\because (\iota)^{2}=-1\}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{18+12\iota -2}{10}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{16+12\iota}{10}}[/tex]
[tex]{:\implies \quad z=\sf \dfrac{16}{10}+\dfrac{12\iota}{10}}[/tex]
[tex]{:\implies \quad {\bf \therefore}\quad \underline{\underline{z=\bf \dfrac{8}{5}+\dfrac{6}{5}\iota}}}[/tex]
Hence , Option B) (8/5) + (6/5)i is correct :D
