Respuesta :

alinakincsem

Answer:

[tex] \frac { 80 + 5i } { 89} [/tex]

Step-by-step explanation:

We are given the following expression to simplify:

10 over quantity of 8 minus 5 i --> [tex] \frac { 10 } { 8 - 5i } [/tex]

[tex] \frac { 10 } { 8 - 5i } [/tex] × [tex] \frac { ( 8 + 5i ) } { ( 8 + 5i ) } [/tex]

[tex] 10 [/tex] × [tex] \frac { ( 8 + 5i ) } { 64 + 25 } [/tex]

[tex] \frac { 80 + 5i } { 89} [/tex]

Therefore, the simplified version of the given expression is [tex] \frac { 80 + 5i } { 89} [/tex].

gmany

Answer:

[tex]\large\boxed{\dfrac{10}{8-5i}=\dfrac{80}{89}+\dfrac{50}{89}i}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\(a-b)(a+b)=a^2-b^2\\\\i=\sqrt{-1}\to i^2=-1\\\\\text{distributive property}\ a(b+c)=ab+ac\\-----------------------------\\\\\dfrac{10}{8-5i}=\dfrac{10}{8-5i}\cdot\dfrac{8+5i}{8+5i}=\dfrac{10(8+5i)}{(8-5i)(8+5i)}\\\\=\dfrac{(10)(8)+(10)(5i)}{8^2-(5i)^2}=\dfrac{80+50i}{64-5^2i^2}=\dfrac{80+50i}{64-25(-1)}\\\\=\dfrac{80+50i}{64+25}=\dfrac{80+50i}{89}=\dfrac{80}{89}+\dfrac{50}{89}i[/tex]