Question

Simplify the following expression into the form a + bi, where a and b are rational numbers.

-2i(7-4i)+(3+i)(-2+2i)

Answer 1

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 2

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

Explanation:

The given expression is

`-2i(7-4i)+(3+i)(-2+2i)`

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

Using distributive property we get

`-2i(7)-2i(-4i)+3(-2+2i)+i(-2+2i)`

`-14i+8i^2+3(-2)+3(2i)+i(-2)+i(2i)`

`-14i+8i^2-6+6i-2i+2i^2`

Combine like terms.

`10i^2-10i+6`

Substitute
`i^2=-1`,

`10(-1)-10i-6`

`-10-10i-6`

Combine like terms.

`-16-10i`

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