Results 1 to 5 of 5

Math Help - Two complex number problems!

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    5

    Two complex number problems!

    Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

    I have to solve this two problems:

    1. Find  Re(z)=?  Im(z)=?

    if:

    z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}

    For first problem i don't have a clue how to come to a solution.

    2. Find |z+1|+z+i=0

    I know that |Z|=\sqrt{x^2+y^2} but, what is |z+1|?

    Thank you very much and sorry for my english.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by TheJoker View Post
    Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

    I have to solve this two problems:

    1. Find  Re(z)=?  Im(z)=?

    if:

    z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}

    For first problem i don't have a clue how to come to a solution.
    I think you're missing something in this problem...should something be in front of the minus sign?

    2. Find |z+1|+z+i=0

    I know that |Z|=\sqrt{x^2+y^2} but, what is |z+1|?

    Thank you very much and sorry for my english.
    \left|z+1\right|=\left|(x+1)+iy\right|=\sqrt{(x+1)  ^2+y^2}

    From there, you'll get the system of equations (after comparing real and complex coefficients):

    \left\{\begin{array}{l}x^2+3x+1+y^2=0\\ y=-1\end{array}\right.

    Then solve the system (you'll get two solutions).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    5
    Hi Chris,

    I rechecked the first problem and I'm not missing anything. It's OK.

    Thank you for second solution.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,405
    Thanks
    1328
    Quote Originally Posted by TheJoker View Post
    Because it's my first post on this forum, I would like to thank everyone who contributed to create such a wonderful forum.

    I have to solve this two problems:

    1. Find  Re(z)=?  Im(z)=?

    if:

    z=\sqrt[3]{\frac{2}{-\sqrt{2+i\sqrt{2}}}}
    For first problem i don't have a clue how to come to a solution.
    z^3= -\frac{2}{2+i\sqrt{3}}
    z^3= -\frac{4+ 2i\sqrt{3}}{7}
    Write that in "polar form" with r= \frac{2\sqrt{5}}{7}, \theta= 0.227\pi and use DeMoivre's formula to solve for z.


    2. Find |z+1|+z+i=0

    I know that |Z|=\sqrt{x^2+y^2} but, what is |z+1|?

    Thank you very much and sorry for my english.
    Let z= a+ bi. Then |z+1|= |a+1+ bi|= \sqrt{(a+1)^2+ b^2}

    Your English is excellent. Far better than my (put language of your choice here)!
    Last edited by mr fantastic; November 30th 2009 at 02:57 AM. Reason: Added quote tag, added a latex tag.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    5
    Thank you very much HallsofIvy.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A few complex number problems
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 3rd 2012, 02:04 PM
  2. Two complex number problems!
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 30th 2010, 06:36 AM
  3. A few complex number problems
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 1st 2010, 08:02 AM
  4. Replies: 1
    Last Post: October 2nd 2010, 01:54 PM
  5. Replies: 3
    Last Post: September 13th 2010, 11:13 AM

Search Tags


/mathhelpforum @mathhelpforum