Results 1 to 8 of 8

Math Help - complex number problem

  1. #1
    Senior Member
    Joined
    Sep 2009
    Posts
    300

    complex number problem

    Hello I need to get the argument of the complex number
    z=2+3i
    in radians I cant seem to get it in radians?
    i get 56.3 degrees is this correct first of all ?
    Please
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by wolfhound View Post
    Hello I need to get the argument of the complex number
    z=2+3i
    in radians I cant seem to get it in radians?
    i get 56.3 degrees is this correct first of all ?
    Please
    You are correct. In the complex plane you can use an Argand diagram with the horizontal axis being real and the vertical axis being imaginary


    To find an answer in radians evaluate \arctan \left(\frac{3}{2}\right) using the radians mode on your calculator

    Wolfram says Wolfram's Answer which agrees with my calculator
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328
    If you can get the answer in degrees, why in the world can't you get it in radians? Either set your calculator to "radian" mode or multiply your answer, in degrees, by \frac{\pi}{180}= \frac{3.1415926}{180} to change to radians.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by wolfhound View Post
    Hello I need to get the argument of the complex number
    z=2+3i
    in radians I cant seem to get it in radians?
    i get 56.3 degrees is this correct first of all ?
    Please
    Note that the argument of z is

    Arg(2+3i) = tan^{-1}3/2 = 56.3

    I'm sure there's a way to do this with special triangles, but I forget. Instead we will simply convert degrees to radians

    Radians = (PI * Degrees ) / 180

     (56.3*pi)/180=.9826
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Sep 2009
    Posts
    300
    Thanks I can get 0.9826 ,
    The thing thats worrying me is I have to write my answers in polar form in a test tomorrow and all the questions we have done in class, have fancy answers like 2Pi/3 in the polar form
    so its ok to write r(cos0.9826 + isin0.9826) ?
    thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by wolfhound View Post
    Thanks I can get 0.9826 ,
    The thing thats worrying me is I have to write my answers in polar form in a test tomorrow and all the questions we have done in class, have fancy answers like 2Pi/3 in the polar form
    so its ok to write r(cos0.9826 + isin0.9826) ?
    thanks
    Are you allowed calculators? If not then this becomes a problem. But I truly don't see a way of making 56 degrees into a nice number in radians.

    So yes, that is correct.

    If your teacher wants W as a polar representation then that is perfectly fine. Unless the question explicitly states "find a nice representation of this in radians" or something to that effect, what you have above is correct.

    It's just not pretty :P
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Sep 2009
    Posts
    300
    I see thanks ,one more question please , how do I write z=2i
    in polar form?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by wolfhound View Post
    I see thanks ,one more question please , how do I write z=2i
    in polar form?
    Remember that the modulus is of the form

    z=a + bi

    In this case a = 0

    So our argument is simply

    Arg(z) = \sqrt{2} = pi/4

    Then put that into polar. Pi/4 comes from special triangles.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A complex problem on number
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 14th 2010, 04:22 AM
  2. Complex Number problem
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: January 6th 2010, 03:56 AM
  3. Another complex number problem.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 3rd 2009, 06:58 AM
  4. Complex Number Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 6th 2009, 11:15 PM
  5. Complex number problem...
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 21st 2008, 12:52 PM

Search Tags


/mathhelpforum @mathhelpforum