Question

Escreva na forma z=a+bi o número complexo (2+i)²/1+i

Answer 1

$z=(2+i)(2+i)\\z=4+2i+2i+i^{2}\\z=4+4i+(-1)\\z=4-1+4i\\z=3+4i$
Espero ter ajudado!! :)

Answer 2

Z = a + bi, sendo que a, b ∈ IR; i ∈ Z.

$Z= \frac{(2+i)^2}{1+i} \\ \\ Z=\frac{(2+i)*(2+i)}{1+i} \\ \\ Z= \frac{4+2i+2i+i^2}{1+i} \\ \\ Z= \frac{4+4i+(-1)}{1+i} \\ \\ Z= \frac{4+4i-1}{1+i} \\ \\ Z= \frac{3+4i}{1+i} \\ \\ Z= \frac{3+4i}{1+i}* \frac{1-i}{1-i} \\ \\ Z= \frac{3-3i+4i-4i^2}{1+i-i-i^2}\\\\Z= \frac{3-3i+4i-4i^2}{1-i^2} \\ \\ Z= \frac{3+i-4(-1)}{1-(-1)} \\ \\ Z= \frac{3+i+4}{1+1} \\ \\ Z= \frac{7+i}{2} \\ \\ Z= \frac{7}{2} +\frac{i}{2}\\\\Z=3,5+0,5i$