Question

I need help with number 17 pls I need the equation plssimplify

Answer 1

-2

Step-by-step explanation:
`17)\text{ }\frac{-4\text{ + 2i}}{2\text{ - i}}`

To simplify, we will use the conjugate of the denominator

conjugae of 2 - 1 = 2 + i

Multiply the conjugate of the denominator to the numerator and denominator:

`\begin{gathered} \frac{-4\text{ + 2i}}{2\text{ - i}}\text{ }*\frac{2+i}{2\text{ + i}} \\ =\text{ }((-4+2i)(2+i))/((2-i)(2+i)) \\ \text{Expand:} \\ =\text{ }(-4(2+i)+2i(2+i))/((2-i)(2+i)) \end{gathered}`
`\begin{gathered} =\text{ }(-8-4i+4i+2i^2)/((2-i)(2+i)) \\ \\ \text{expand the denominator:} \\ =\text{ }(-8-4i+4i+2i^2)/(2(2+i)-i(2+i)) \\ =\text{ }(-8-4i+4i+2i^2)/(4+2i-2i-i^2) \end{gathered}`
`\begin{gathered} In\text{ complex number, } \\ i^2\text{ = -1} \\ \text{substitute for i}^2 \\ =\text{ }(-8-4i+4i+2i^2)/(4+2i-2i-i^2)\text{ = }=\text{ }(-8-4i+4i+2(-1))/(4+2i-2i-(-1)) \\ =\text{ }(-8+0+2(-1))/(4+0-(-1))\text{ = }(-8-2)/(4+1)\text{ } \\ =\text{ }(-10)/(5) \\ =\text{ -2} \end{gathered}`

The simplified answer is -2