How Do You Solve Complex Equations Involving Absolute Values?

[transgalactic]

http://img353.imageshack.us/img353/672/85253506or3.gif

in normal equation i equalize the "Real" part with the real part
and the "Im" part with the I am part on the other size of the equation
but here there is | | part

which makes every thing a^2 + b^2 and it turns everything to "real"

??

 

[berkeman]

Why do you have 2 equations and 1 unknown?

 

[transgalactic]

"z" is a complex number which i need to split into a real and imaginary parts

 

[berkeman]

Sorry, I'm not tracking you on this one. Why are there two equations shown?

WW = XX = YY

That overconstrains the solution for z. One equation should be enough to solve for z, it would seem?

 

[transgalactic]

z is a complex number
its not a single variable
z=a+ib
i need to find Z

 

[berkeman]

Ah, I think I see now.

in normal equation i equalize the "Real" part with the real part
and the "Im" part with the I am part on the other size of the equation
but here there is | | part

which makes every thing a^2 + b^2 and it turns everything to "real"

Try squaring the whole side of each equation, and not the individual terms. You will still have real and imaginary parts to the squared equations.

 

[berkeman]

So like

z+i = z-1

z^2 + 2iz - 1 = etc. and gather terms on one side = 0

Then do the other equation, and you should be able to solve for RE{z} and Im{z}.

 

[Dick]

It's probably easier to split it into to real and imaginary parts right off the bat. If z=a+bi, what is |z+i| in terms of a and b? How about the other two absolute values?

 

[JANm]

You want the absolute value of z_1 = z+1= a+(b+1)*i ?

 

[Dick]

You want the absolute value of z_1 = z+1= a+(b+1)*i ?

I'm going to guess you meant z+i=a+(b+1)*i, not z+1.