Results 1 to 3 of 3

Math Help - Write this complex number on the form a + bi

  1. #1
    Junior Member
    Joined
    Jul 2012
    From
    Earth
    Posts
    56

    Write this complex number on the form a + bi

    I'm dealing with this problem where I'm to write the complex number below on the form a + bi.

    \frac {\sqrt{2+i}}{\sqrt{2-i}}

    I've tried writing it as

    \sqrt {\frac {2+i}{2-i}}

    Then I tried multiplying by the conjugate, writing it using polar coordinates, considering the squre root as an exponent of 0.5 etc. However, I just kept reaching a dead end. The expression is supposedly equal to

    \fr {2\sqrt{5}}{5} + \fr {i\sqrt{5}}{5}

    How do I go about?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,454
    Thanks
    1868

    Re: Write this complex number on the form a + bi

    You suspect have misread the answer you are supposed to get. It should be 2\sqrt{5}/5+ i\sqrt{5}/5 or 2\frac{\sqrt{5}}{5}+ i\frac{\sqrt{5}}{5} either of which is equal to \frac{2}{\sqrt{5}}+ \frac{i}{\sqrt{5}}.

    You get that by, as you say, multiplying by the conjugate. Then "rationalize the denominator".
    Last edited by HallsofIvy; October 13th 2012 at 03:03 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1

    Re: Write this complex number on the form a + bi

    Quote Originally Posted by MathCrusader View Post
    I'm dealing with this problem where I'm to write the complex number below on the form a + bi.
    \frac {\sqrt{2+i}}{\sqrt{2-i}}
    I've tried writing it as
    \frac {2\sqrt{5}}{5} + \frac {i\sqrt{5}}{5}
    How do I go about?
    \frac {\sqrt{2+i}}{\sqrt{2-i}}\frac {\sqrt{2-i}}{\sqrt{2-i}}=\frac {\sqrt{5}}{2-i}=\frac {2\sqrt{5}+\sqrt{5}i}{5}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 25th 2012, 02:57 PM
  2. Complex number(exponential form)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2009, 03:35 AM
  3. Replies: 3
    Last Post: March 1st 2009, 08:11 PM
  4. HELPP Write complex number in polar form.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 14th 2008, 01:43 PM
  5. Replies: 7
    Last Post: November 28th 2008, 05:56 AM

Search Tags


/mathhelpforum @mathhelpforum