Results 1 to 3 of 3

Math Help - Complex Number question

  1. #1
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1

    Complex Number question

    Hi everyone, anyone fancy helping out on yet another question

    A complex number z is represented by the point P on an Argand diangram, |z-5-12i| = 3.

    a. Sketch the locus of P.

    This I could do, circle, centre (5, 12), radius of 3.

    b. Find the maximum and minimum values for |z|.

    For this I found the distance of the centre of the circle from the origin, and then \pm the radius to get 10 and 16, is this correct?

    c. Find the min and max values for arg{z} in radians to 2dp.

    Argument is tan^{-1}{\frac{12}{5}}, but not sure where to go to get the max and min values from here?

    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member alunw's Avatar
    Joined
    May 2009
    Posts
    188
    b) is correct but you probably need to justify your answer better. After all you can't usually just add and subtract lengths like this.

    c) Since the circle does not contain the origin, and does not pass through the x axis the minimum and maximum values of the argument occur at the points where lines through the origin are tangent to the circle. Let the centre of the circle be C and the point of tangency be P. angle OPC is a right angle. You know the length of OC and CP, so you have a right angled triangle for which CP/OC is the sine of angle POC. Given that you already know the argument of C you can then easily find the arguments of the two points of tangency. So you can find the answer without actually finding the coordinates of the two tangent points!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Thank you! Didn't think of doing that
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex number question
    Posted in the Algebra Forum
    Replies: 9
    Last Post: March 12th 2011, 01:20 AM
  2. Another Complex Number Question
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 30th 2009, 03:46 AM
  3. complex number question
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 22nd 2009, 01:40 AM
  4. can anyone help me complex number question?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 20th 2009, 10:28 AM

Search Tags


/mathhelpforum @mathhelpforum