Solve |z|+z=2+i

Dear Student,

Let z = x + iy 
zx2+y2

z + z = 2 + i
x2+y2 + x + iy = 2 + i
Therefore, y = 2 and x2+y2 + x = 2
x2+22 + x = 2
x2+22 = 2 - x
Squaring both sides
x2 + 4 = 4 - 4x + x2 
0 = - 4x
x = 0

Hence, z = 2i

Regards
 

  • 2
Also the answer is shown to be 3/4 + i. Could you please explain how it is done?
  • 7
I think the answer should be  i=2z-2
  • -2
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