Question

Dados z1= 4+i, z2= -1+2i e z3= 5-3i, calcule:
a) z1/z2
b) z1-z3
c) (z1+z2)*z3

Answer 1

Olá,

z₁ = 4 + i
z₂ = -1 + 2i
z₃ = 5 - 3i

a) z₁/z₂
$\frac{4+i}{-1 + 2i} * \frac{(-1 - 2i)}{(-1-2i)} \\\\ \frac{-4 - 8i -i -2i^2}{(-1)^2 - (2i)^2} \\\\ \frac{-4 -9i-2*(-1)}{1-4*(-1)} \\\\ \frac{-4-9i+2}{1+4} \\ \\ \frac{-2-9i}{5} \\\\ -\frac{2}{5} - \frac{9i}{5}$

b) z₁ - z₃
(4 + i) - (5 - 3i)
4 - 5 + (i + 3i)
-1 + 4i

c) (z₁ + z₂)*z₃
[(4 + i) + (-1 + 2i)]*(5 - 3i)
[(4 - 1) + (i + 2i)]*(5 - 3i)
(3 + 3i)*(5 - 3i)
3*5 -3*3i + 3i*5 - 3i*3i
15 - 9i + 15i - 9i²
15 + 6i - 9*(-1)
15 + 6i + 9
24 + 6i

Bons estudos ;)