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Boa tarde!
Solução!
![\left \dfrac{8+i}{2-i} \right \\\\\\\
\left ( \dfrac{8+i}{2-i} \times \dfrac{2+i}{2+i} \right )\\\\\\\
\left ( \dfrac{16+8i+2i+i ^{2}}{4+2i-2i-i^{2} } \right )\\\\\\\
\left ( \dfrac{16+10i+i ^{2}}{4-i^{2} } \right )\\\\\\\
Lembrado:i^{2}=-1~~substituindo!\\\\\\\
\left ( \dfrac{16+10i-1}{4-(-1)} \right )\\\\\\\
\left ( \dfrac{16+10i-1}{4+1} \right )\\\\\\\
\left ( \dfrac{16-1+10i}{5} \right )\\\\\\\
\left ( \dfrac{15+10i}{5} \right )\\\\\\\
\left ( \dfrac{5(3+2i)}{5} \right )\\\\\\\](https://tex.z-dn.net/?f=%5Cleft+%5Cdfrac%7B8%2Bi%7D%7B2-i%7D+%5Cright+%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B8%2Bi%7D%7B2-i%7D+%5Ctimes+%5Cdfrac%7B2%2Bi%7D%7B2%2Bi%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B16%2B8i%2B2i%2Bi+%5E%7B2%7D%7D%7B4%2B2i-2i-i%5E%7B2%7D+%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B16%2B10i%2Bi+%5E%7B2%7D%7D%7B4-i%5E%7B2%7D+%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0ALembrado%3Ai%5E%7B2%7D%3D-1%7E%7Esubstituindo%21%5C%5C%5C%5C%5C%5C%5C+%0A%5Cleft+%28+%5Cdfrac%7B16%2B10i-1%7D%7B4-%28-1%29%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cleft+%28+%5Cdfrac%7B16%2B10i-1%7D%7B4%2B1%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B16-1%2B10i%7D%7B5%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B15%2B10i%7D%7B5%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B5%283%2B2i%29%7D%7B5%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A "\left \dfrac{8+i}{2-i} \right \\\\\\\
\left ( \dfrac{8+i}{2-i} \times \dfrac{2+i}{2+i} \right )\\\\\\\
\left ( \dfrac{16+8i+2i+i ^{2}}{4+2i-2i-i^{2} } \right )\\\\\\\
\left ( \dfrac{16+10i+i ^{2}}{4-i^{2} } \right )\\\\\\\
Lembrado:i^{2}=-1~~substituindo!\\\\\\\
\left ( \dfrac{16+10i-1}{4-(-1)} \right )\\\\\\\
\left ( \dfrac{16+10i-1}{4+1} \right )\\\\\\\
\left ( \dfrac{16-1+10i}{5} \right )\\\\\\\
\left ( \dfrac{15+10i}{5} \right )\\\\\\\
\left ( \dfrac{5(3+2i)}{5} \right )\\\\\\\")
Boa tarde!
Bons estudos!
Solução!
Boa tarde!
Bons estudos!
Issam1969:
Obrigado !!
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