Imaginary Numbers

[ECHOSIDE]

Again, I feel the need to call upon my nerdy brethren for help with an equation.
This is Intermediate Algebra (late high school / early college).

4/(2x+i) - 1/(x-i) = 2/(x+i)

If there were no imaginary numbers here, I think I'd be more comfortable. Imaginary numbers are a new concept to me, and I'm not sure how to manipulate them. Every rabbit hole I chase down with this one leaves me more frustrated. Does someone know how to attack this thing?

Thanks for any help you can provide!

 

[Psychoteddy]

One thing you can try to help you out is replacing "i" with √-1 and remembering that i*i = -1.

Unfortunately, my algebra skills are waning and I don't have a solution for you, but I thought I'd try to help as much as I can. I know this strategy helped me a lot in HS algebra.

 

[Sequences]

You would want to isolate the imaginary numbers and real numbers.

4/(2x+i) - 1/(x-i) = 2/(x+i)
(4x-4i-2x-i)/[(2x+i)(x-i)] = 2/(x+i)
(2x-5i)(x+i) = 2(2x+i)(x-i)
2x^2+2xi-5xi+5 = 4x^2-4xi+2xi+2
2x^2-3xi+5 = 4x^2-2xi+2
0=2x^2+xi-3

I guess you could use the quadratic equation to solve?

 

[NoCanDo]

Sequences workings are correct.
I don't know if you can use complex and imaginary coefficients in the quadratic equation?
You may be able to, although I'm unsure.

 

[NoCanDo]

Ahh, I stand corrected - you are able to use complex and imaginary coefficients in the quadratic equation, it can just get a bit messy.