Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distance between two complex numbers

  1. Jun 27, 2004 #1
    Hi...i was wondering if someone could confirm if what i have below is correct...thanks...sorry i can't present a diagram...

    z(1) = x + iy and z(2) = x(2) + iy(2) are represented by the vectors OP and OQ on an argand diagram...(O is the origin)...imagine the argand diagram...the upper left hand quadrant...(OQ has an argument of say 30 degrees and OP has an argument of 45 degrees - these pieces of information are not relevant anyway)...

    is the following correct...

    vector OP + vector PQ = vector OQ...

    then vector PQ = vector OQ - vector OP

    then vector PQ = |z(2) - z(1)|...

    1. was wondering if my notation and understanding here is correct...i used algebra in the second line so i was wondering if that is legit...???...

    2. is it correct to say in the last line the vector = the magnitude
  2. jcsd
  3. Jun 27, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    That's fine.
    That's wrong. You should have:

    [tex]\vec{PQ} = z_2 - z_1[/tex]

    [tex]|\vec{PQ}| = |z_2 - z_1|[/tex]

    Or, in plain text:

    vector PQ = z(2) - z(1)
    |vector PQ| = |z(2) - z(1)|
  4. Jun 28, 2004 #3
    Hi...thank you very much...

    i said in my earlier post...

    and it was said that it should be...

    1. isn't that the same thing...

    that vector PQ = the magnitude of [z(2) - z(1)]...???...
  5. Jun 28, 2004 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    No, it is not the same thing: |vector PQ| is a number (the length of the vector PQ), not a vector.

    Likewise "vector PQ" is a vector while "the magnitude of [z(2)-z(1)]" is a number.
  6. Jun 28, 2004 #5
    thank you very much...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?