Complex numbers problems | Solving equations using polar form

[Broken Steel]

Homework Statement

Solve the equation in the complex numbers set (this is as best as i could translate since English is not my native language :D)

\left|z\right|-z=1+2i

Homework Equations

|z|=sqrt{x^2+y^2}

z=x+iy

The Attempt at a Solution

Well i started by supposing y=1 and then i get sqrt{x^2+1}-x=1-i+x
i tried to square the whole equation but i end up with nothing.. So what should I do??

Oh and the solution is 3/2 - 2i

 

[tiny-tim]

Hi Broken Steel!

(have a square-root: √ and a phi: φ and try using the X² tag just above the Reply box )

Hint: re^iφ

 

[eumyang]

How about this way?
\left|z\right|-z=1+2i

Replace the |z| and z by the values you specified above:
\sqrt{x^2+y^2} - (x + yi) = 1 + 2i

Remove the parentheses, and then equate the real coefficients and the imaginary coefficients.

 

[Apphysicist]

Hi Broken Steel!

(have a square-root: √ and a phi: φ and try using the X² tag just above the Reply box )

Hint: re^iφ

Likes this method because it is more useful for dealing with complex numbers.

Also, eumyang's is probably a more familiar method.