Homework Help

How solve in complex plane equation z+|z|=8-4i?

user profile pic

yapayapa | Honors

Posted September 4, 2013 at 5:04 PM via web

dislike 0 like

How solve in complex plane equation z+|z|=8-4i?

Tagged with equation complex, math

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 4, 2013 at 5:10 PM (Answer #1)

dislike 0 like

The equation z + |z| = 8 - 4i has to be solved.

If z = a + i*b, |z| = `sqrt(a^2 + b^2)`

`a + i*b + sqrt(a^2 + b^2) = 8 - 4i`

=> b = -4 and `a + sqrt(a^2 + b^2) = 8`

`a +sqrt(a^2 + 16) = 8 `

=> `64 + a^2 - 16a = a^2 + 16`

=> 16a = 48

=> a = 3

The complex number is 3 - 4i

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes