Question

sejam: Z=4+5i e W=2+3i. calculeZ/W

Answer 1

No assunto de numeros complexos o i tem valor igual a -1.
Logo,
Z = 4 - 5 = -1
W = 2 - 3 = -1

Z/W = 1

Answer 2

$Z=4+5i \\ W=2+3i \\ \\ \\ \dfrac{Z}{W} = \dfrac{4+5i}{2+3i} \\ \\ \\ \dfrac{Z}{W}= \dfrac{4+5i}{2+3i} \cdot \dfrac{2-3i}{2-3i} \\ \\ \\ \dfrac{Z}{W} = \dfrac{(4+5i)(2-3i)}{(2+3i)(2-3i)} \\ \\ \\ \dfrac{Z}{W} = \dfrac{8-12i+10i-15i^2}{4-6i+6i-9i^2}$


Lembre-se que i² = -1  :


$\dfrac{Z}{W} = \dfrac{8-2i - 15i^2}{4-9i^2} \\ \\ \\ \dfrac{Z}{W} = \dfrac{8-2i - 15\cdot(-1)}{4-9\cdot(-1)} \\ \\ \\ \dfrac{Z}{W} = \dfrac{8-2i - (-15)}{4-(-9)} \\ \\ \\ \boxed{\dfrac{Z}{W} = \dfrac{23-2i}{13}}$