1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find no. of Complex Numbers

  1. Oct 3, 2012 #1

    utkarshakash

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Find the number of complex numbers satisfying [itex] |z|=z+1+2i[/itex]


    2. Relevant equations


    3. The attempt at a solution
    Let z=x+iy
    |x+iy| = (x+1)+i(2+y)
    Squaring and taking modulus
    |[itex]\sqrt{x^{2}+y^{2}}|^{2} = |(x+1)+i(2+y)|^{2}[/itex]
    [itex]x^{2}+y^{2} = (x+1)^{2}+(2+y)^{2}[/itex]
    Rearranging and simplifying I get
    2x+4y+5=0

    Now what to do next? Also Is there any other way to solve this question?
     
  2. jcsd
  3. Oct 3, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You seem to have missed an important point- the absolute value of a complex number is real. Since the left side of the equation is real, the right side must be. z must be of the form z= x- 2i so that z+ 1+ 2i= x+1. What you did was correct but how many points on the line 2x+ 4y+ 5= 0 also satisfy y= -2?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find no. of Complex Numbers
Loading...