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I've been beating my head up on this equation, so I thought I'd try here to see if someone could help me. In the equation

(sqrt{32}(2x-d))^-4 = (-d/2 - 1/2 )^2 + sqrt{(1+d)^2 + d/4}/4

Where the right hand side is my attempt to solve for d out of the magnitude |z| of a complex number. You can see by looking at the right hand side (if you look carefully) how the right side used to be expressed in the form

|z|=r=sqrt{x^2+y^2}, where z = x + yi,

the magnitude (modulus) of a complex number. I got kind of tangled up with this, but I've left it where I got stuck, as it looks like an algebraic solution is possible (a polynomial of sorts), but I see I am missing some information on how to proceed and I wanted to see if someone could help me where I left off. And no, this is not a homework question. In short, my question is, with so many power and sqrt's, how does one begin to solve for d, as the only other variable is x, which I already have a solution for. Is this a 3rd or 4th degree polynomial, or is it simpler? Or is it more complicated still?

Any help and pointing me in the right direction? I've tried many attempts, but feel there might be a simple method I am just over looking...or perhaps some aspect of the mathematics that I have not been involved with.

Thanks,

Jeff

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# On solving for a variable in the magnitude of a complex number

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