let a be a real number such that the following product is also equal to a real number. (a - 4i)(-6 + 4i)…

let a be a real number such that the following product is also equal to a real number. (a - 4i)(-6 + 4i) what is the value of a? a =

let a be a real number such that the following product is also equal to a real number. (a - 4i)(-6 + 4i) what is the value of a? a =

Answer

Explanation:

Step1: Expandir el producto

$$(a - 4i)(-6 + 4i)=a(-6)+a(4i)-4i(-6)-4i(4i)$$ $$=-6a + 4ai + 24i-16i^{2}$$ Como (i^{2}=-1), entonces: $$=-6a + 4ai + 24i + 16$$ $$=(-6a + 16)+(4a + 24)i$$

Step2: Igualar la parte imaginaria a cero

Como el producto es un número real, la parte imaginaria debe ser cero. (4a+24 = 0) Resolviendo para (a): (4a=-24) (a=\frac{-24}{4})

Answer:

(a=-6)