Real Value of x in Complex Equation?

[Alec]

Homework Statement

Decide the real value of x making Re(10 / x+4i) = 1

Homework Equations

I know that you can extend the equation with x-4i.

The Attempt at a Solution

But then the equation looks like this: (10x-40i) / (x^2 + 16) = 1
I don't know how to get rid of the -40i to make it into a real equation.

Any help would be valuable!

 

[HallsofIvy]

$$\frac{10x-40i}{x^2+ 16}= \frac{10x}{x^2+16}-i\frac{40}{x^2+ 16}$$

 

[daveb]

It says the real part of (10x - 40i)/(x^2 + 16) = 10x/(x^2+16) - 40i/(x^+16). Take the real part of that and set it equal to 1, and solve for x.