How to solve this complex number question

1. Nov 20, 2008

transgalactic

http://img353.imageshack.us/img353/672/85253506or3.gif [Broken]

in normal equation i equalize the "Real" part with the real part
and the "Im" part with the Im 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"

??

Last edited by a moderator: Apr 23, 2017 at 10:12 PM
2. Nov 20, 2008

Staff: Mentor

Why do you have 2 equations and 1 unknown?

3. Nov 20, 2008

transgalactic

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

4. Nov 20, 2008

Staff: Mentor

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?

5. Nov 20, 2008

transgalactic

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

6. Nov 20, 2008

Staff: Mentor

Ah, I think I see now.

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.

7. Nov 20, 2008

Staff: Mentor

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}.

8. Nov 20, 2008

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?

9. Nov 21, 2008

JANm

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

10. Nov 21, 2008

Dick

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