Respuesta :

kudzordzifrancis

ANSWER

[tex](4 + 9i)(7 - 4i) = 64 + 47i [/tex]

EXPLANATION

The given complex number expression is:

[tex](4 + 9i)(7 - 4i)[/tex]

We expand using the distributive property to get;

[tex](4 + 9i)(7 - 4i) = 4(7 - 4i) + 9i(7 - 4i)[/tex]

[tex](4 + 9i)(7 - 4i) = 28- 16i + 63i - 36 {i}^{2} [/tex]

Recall that,

[tex] {i}^{2} = - 1[/tex]

Our expression now simplifies to:

[tex](4 + 9i)(7 - 4i) = 28 + 47i + 36 [/tex]

[tex](4 + 9i)(7 - 4i) = 64 + 47i [/tex]

luisejr77

Answer: [tex]64+47i[/tex]

Step-by-step explanation:

Given the Complex numbers multiplication:

[tex](4+9i)(7-4i)[/tex]

You need to follow these steps:

1. Apply Distributive property:

[tex](4+9i)(7-4i)=(4)(7)+(4)(-4i)+(9i)(7)+(9i)(-4i)=28-16i+63i-36i^2[/tex]

2. You need to remember that:

[tex]i=\sqrt{-1}\\\\i^2=-1[/tex]

Then, you need to substitute [tex]i^2=-1[/tex]:

 [tex]28-16i+63i-36(-1)=28-16i+63i+36[/tex]

3. Finally, add the like terms:

[tex]64+47i[/tex]

Otras preguntas