Respuesta :

The answer is -16 - 10i.

Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)

Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²

Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i

Answer:

The simplified value of the given expression is -16-10i.

Step-by-step explanation:

The given expression is

[tex]-2i(7-4i)+(3+i)(-2+2i)[/tex]

We need to convert the expression into the form a + bi, where a and b are rational numbers.

Using distributive property we get

[tex]-2i(7)-2i(-4i)+3(-2+2i)+i(-2+2i)[/tex]

[tex]-14i+8i^2+3(-2)+3(2i)+i(-2)+i(2i)[/tex]

[tex]-14i+8i^2-6+6i-2i+2i^2[/tex]

Combine like terms.

[tex]10i^2-10i+6[/tex]

Substitute [tex]i^2=-1[/tex],

[tex]10(-1)-10i-6[/tex]

[tex]-10-10i-6[/tex]

Combine like terms.

[tex]-16-10i[/tex]

Therefore the simplified value of the given expression is -16-10i.

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