Question

Calcule o quociente de (3+2i) por (4-3i)


a) 6 + 17i
______ =
7


b) 17 + 6i
______ =
25


c) 6 + 17i
______ =
25


d) 6 + 17i
______ =
8
​

Answer 1

Explicação passo-a-passo:

$Z=\dfrac{3+2i}{4-3i}$

Multiplicamos o numerador e o denominador pelo conjugado do denominador, ou seja, $4+3i$.

$Z=\dfrac{3+2i}{4-3i}.\dfrac{4+3i}{4+3i} \\\\\\Z=\dfrac{3.4+3.3i+2i.4+2i.3i}{4^{2}-(3i)^{2}}\\\\\\Z=\dfrac{12+9i+8i+6i^{2} }{16-9i^{2}}\\\\\\Z=\dfrac{12+17i+6.(-1) }{16-9.(-1)}\\\\\\Z=\dfrac{12+17i-6 }{16+9}\\\\\\Z=\dfrac{6+17i }{25}$

Resposta C