Question

Evaluate (10 – 41) ÷ (5 + 1).

Answer 1

Explanation:

option B is correct answer

Answer 2

`\((10 - 4i) / (5 + i) = (23)/(13)-(15i)/(13)`, which can be further simplified if needed.

To evaluate the expression
`\((10 - 4i) / (5 + i)\)`, we'll multiply both the numerator and denominator by the conjugate of the denominator to rationalize the denominator.

The conjugate of
`\(5 + i\) is \(5 - i\)`.

`\((10 - 4i) / (5 + i) = ((10 - 4i) * (5 - i))/((5 + i) * (5 - i))\)`

Let's perform the multiplication:

Numerator:

`\[ (10 - 4i) * (5 - i) = 50 - 10i - 20i + 4i^2 \]`

`\[ = 50 - 30i - 4 \] (Remember that \(i^2 = -1\))`

`\[ = 46 - 30i \]`

Denominator:

`\[ (5 + i) * (5 - i) = 25 - 5i + 5i - i^2 \]`

`\[ = 25 - i^2 \]`

`\[ = 25 + 1 \]`

`\[ = 26 \]`

Now, simplify the expression:

`\[ ((10 - 4i) / (5 + i))/((5 + i) / (5 - i)) = (46 - 30i)/(26) =(23)/(13) -(15i)/(13)`