Question

dados los numeros complejos

Z1 = 5+3i

Z5= 3+3i

calcular. division


Z1/Z5 =

Answer 1

Respuesta:

$\dfrac{Z_1}{Z_5}=\dfrac{4-i}{3}$

 

Explicación paso a paso:

Datos:

$Z_1=5+3i\\Z_5=3+3i\\\\\dfrac{Z_1}{Z_5}=?$

 

$\dfrac{Z_1}{Z_5}=\dfrac{5+3i}{3+3i}*\dfrac{3-3i}{3-3i}=\dfrac{(5+3i)(3-3i)}{3^2-(3i)^2}=\dfrac{5*3+5*-3+3i*3+3i*-3i}{9-(-9)}\\\\\\\dfrac{Z_1}{Z_5}=\dfrac{15-15i+9i+9}{18}=\dfrac{24-6i}{18}=\dfrac{6(4-i)}{6(3)}\\\\\\\boxed{\dfrac{Z_1}{Z_5}=\dfrac{4-i}{3}}$