1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Math problem

  1. Nov 14, 2003 #1
    hope to get the idea on how to solve this question.

    the complex number z is given by

    z = 1 + cos (theta) + i sin (theta)

    where -pi < theta < or = +pi

    show that for all values of theta, the point representing z in a Argand diagram is located on a circle. find the centre and radius of the circle.
  2. jcsd
  3. Nov 14, 2003 #2


    User Avatar
    Science Advisor

    If z = 1 + cos (&theta;) + i sin (&theta)

    Then z-1= cos(&theta)+ i sin(&theta;).

    If you represent z as x+ iy then
    (x-1)+ iy= cos(&theta;)+ i sin(&theta;)

    or x- 1= cos(&theta;), y= sin(&theta;)

    Those are parametric equations of a circle with what center and radius?
  4. Nov 15, 2003 #3
    ok. i compare those with the
    y=r sin (&theta)
    x=r cos (&theta)

    so, i know the radius = 1 unit
    but may i know how to find the centre of the circle?

  5. Nov 15, 2003 #4


    User Avatar
    Science Advisor

    It's exactly where the center of the circle given by

    x= r cos &theta;
    y= r sin &theta; is!

    Hint: x2= r2cos2&theta;
    y2= r2sin2&theta;

    What is x2+ y2?

    If that's too complicated, what is (x,y) when &theta;= 0?
    What is (x,y) when &theta;= &pi;?
  6. Nov 15, 2003 #5
    tq. u helped me solved the problem.

    but there is another part of the question which i ahain need some idea.

    --> prove that the real part of (1/z) is (1/2) for all values of [the]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook