SOLUTION: Solve: |z| + z = 2 + i , where z is a complex no.

Looking into equation, you can momentarily conclude that the imaginary part of z is i; in other words, 

z = a + i, where "a" is a real nnumber.


Then |z| = ,  and the original equation implies for the real parts

 + a = 2,

 = 2 - a,   then squaring both sides

 = ,

1 = 4 - 4a,

4a = 4-1 = 3  ====>  a = .


Answer.  z = .