Results 1 to 6 of 6

Math Help - Complex Nuumbers

  1. #1
    Member Awsom Guy's Avatar
    Joined
    Jun 2009
    From
    Mars
    Posts
    186

    Complex Nuumbers

    Hi everybody,

    Find the square roots of the following in cartesian form.
    1+sqrt3i
    I think thats typed right.
    I am not sure how to attempt it.
    The example in my book is too simple and doesn't explain it properly.
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    You have to find two real numbers a and b such as (a+bi)^2=1+i\sqrt{3}

    Square the left side member and we get a^2-b^2+2abi=1+i\sqrt{3}. Then

    \left\{\begin{array}{ll}a^2-b^2=1\\2ab=\sqrt{3}\end{array}\right.

    You can add another equation to the system.

    |(a+bi)^2|=|1+i\sqrt{3}|\Rightarrow a^2+b^2=2.

    Then the system is

    \left\{\begin{array}{ll}a^2-b^2=1\\2ab=\sqrt{3}\\a^2+b^2=2\end{array}\right.

    Find a and b from the first and the third equations. Then choose the signs for a and b such as the second equation is satisfyed.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Awsom Guy's Avatar
    Joined
    Jun 2009
    From
    Mars
    Posts
    186

    Huh

    Sorry but I haven't learnt any of that but I don't get it.
    Can we have a simpler way. I know the eqaution a+root(a^2+b^2)/2
    That is the only thing I know.
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    Quote Originally Posted by Awsom Guy View Post
    Sorry but I haven't learnt any of that but I don't get it. Can we have a simpler way.
    This is the standard way.
    Because 1 + i\sqrt 3  = 2\left( {\cos \left( {\frac{\pi }{3}} \right) + i\sin \left( {\frac{\pi }{3}} \right)} \right) the two square roots are:
    \sqrt 2 \left( {\cos \left( {\frac{\pi }<br />
{6}} \right) + i\sin \left( {\frac{\pi }<br />
{6}} \right)} \right)\;\& \,\sqrt 2 \left( {\cos \left( {\frac{{ - 5\pi }}<br />
{6}} \right) + i\sin \left( {\frac{{ - 5\pi }}<br />
{6}} \right)} \right)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member Awsom Guy's Avatar
    Joined
    Jun 2009
    From
    Mars
    Posts
    186
    What about the formula a+sqrt(a^2+b^2)/2.
    I am sopposed to find x and then y. Then bring them together to make a cartesian formed equation like 2+i and -2-i.
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    If you analyze the solution by red_dog, you will find what you need.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: November 27th 2011, 12:15 AM
  2. Replies: 3
    Last Post: October 4th 2011, 05:30 AM
  3. Replies: 6
    Last Post: September 13th 2011, 07:16 AM
  4. Replies: 12
    Last Post: June 2nd 2010, 02:30 PM
  5. Replies: 1
    Last Post: March 3rd 2008, 07:17 AM

Search Tags


/mathhelpforum @mathhelpforum