Question

I have used different apps to help me with this question, and none of them have given me any of the options. The teacher told me C is the correct answer, but I cannot find out the math for it. Please help!! :(

Answer 1

The correct answer is C)
`\boxed{(3-4i)/(2)}]` .

To solve the equation, we can use the following steps:

Multiply both sides of the equation by the complex conjugate of the denominator.

`[(1+7i)/(-2+2i)]` .
`(-2-2i)/(-2-2i)`

=
`((1+7i)(-2-2i))/((-2+2i)(-2-2i))]`

Expand the product in the numerator.

`[((1+7i)(-2-2i))/((-2+2i)(-2-2i))`

=
`[\frac{-2-2i - 14i - 14 i^2} {-4+4+4 i^2}]`

Simplify the numerator and denominator.

`[(-2-2i - 14i + 14)/(-4+4+4 i^2)]`

=
`[(12-16i)/(-4+4 i^2)]`

Note that
`−4+4i^2 =(−1) ^2 +(2i)^2`

=
`(1+2i)(1−2i).`

Dividing both sides by (1+2i)(1−2i), we get the solution.

`[(12-16i)/(-4+4 i^2)]`

=
`\boxed{(3-4i)/(2)}]`