Results 1 to 3 of 3

Thread: Another complex number problem.

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    5

    Another complex number problem.

    Hello forumers,

    While learning complex numbers, i got stuck in this two problems:

    1. $\displaystyle z=2-2i\sqrt3$ and $\displaystyle |z+w|=4$, find $\displaystyle w$ if:

    a) $\displaystyle z+w$ is imaginary number
    b) $\displaystyle z+w$ is real number

    2. $\displaystyle z=1+2i.$ Find $\displaystyle w$ if:

    $\displaystyle Re({\frac{w}{\overline{z}}})=2$ and $\displaystyle Im(z\cdot \overline{w})=2$.

    Thank you.

    3. $\displaystyle z+w=i$. If $\displaystyle |z|=\sqrt2$ and If $\displaystyle |w|=\sqrt5$ find complex numbers z and w.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jul 2009
    Posts
    193
    Thanks
    5
    3.
    z= a+ib, w=c+id

    $\displaystyle |z|^2=a^2+b^2=2$ (1)
    $\displaystyle |w|^2=c^2+d^2=5$ (2)

    z+w=(a+c)+i(b+d)=i

    so a+c=0 and b+d=1
    so c=-a and d=1-b

    so by (1) and (2)

    $\displaystyle a^2+b^2=2$
    and
    $\displaystyle a^2+(1-b)^2=5$

    solving for b;
    b=-1

    d=1-b=2
    $\displaystyle a^2=2-b^2=1$
    so a=1 or -1
    c=-a=-1 or 1

    so z=1-i, w=-1+2i or z=-1-i, w=1+2i
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    5
    Thank you Krahl. I solved 2 remaining problems.

    First problem solution is: $\displaystyle w=\frac{\sqrt3}{2}+\frac{1}{2}i$ and $\displaystyle w'=-\frac{\sqrt3}{2}-\frac{1}{2}i$ just for a).
    Second problem solutions is: $\displaystyle w=-2-6i$

    If you have any questions about solution, feel free to ask!

    Thank you.
    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: Nov 14th 2010, 04:22 AM
  2. complex number problem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Mar 16th 2010, 08:45 AM
  3. Complex Number problem
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: Jan 6th 2010, 03:56 AM
  4. Replies: 4
    Last Post: May 21st 2009, 04:11 AM
  5. [SOLVED] Pls help me with this complex number problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 21st 2007, 09:20 AM

Search Tags


/mathhelpforum @mathhelpforum