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Math Help - Complex equations

  1. #1
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    Unhappy Complex equations

    Hi!

    I got stuck on these 2 questions when I tried to do some math:

    A)

    IF its possible solve the equation:

    z− 4iz= 3 + i

    B)

    Write the complex number z in polar form and the form eZ. Reply to this in precise form.
    z= 2 + 2i


    Thx for any help!
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  2. #2
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    A)
    [TR]
    [TD]z− 4iz= 3 + [I]i
    Use z=x+yi transform to (x+4y)+(-4x+y)i=3+i.
    So solve (x+4y)=3~\&~(-4x+y)=1
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  3. #3
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    Re: Complex equations

    Thx for the help but I am totally lost how do I solve (x+4y)=3 and (-4x+y)=1 ?
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  4. #4
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    Thx for the help but I am totally lost how do I solve (x+4y)=3 and (-4x+y)=1 ?
    x+yi=a+bi\text{ if and only if }x=a~\&~y=b
    That is a system of two equations in two unknowns.
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  5. #5
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    Re: Complex equations

    ??? Still don't get it,sorry...
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  6. #6
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    ??? Still don't get it,sorry...
    Can you solve this system:
     \begin{align*}x+4y&=3 \\-4x+y&=1\end{align*}~~?

    If not you need to review basic basic algebra.
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  7. #7
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    Re: Complex equations

    is the answer 13x + y = 3 ?
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  8. #8
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    is the answer 13x + y = 3 ?
    You are not ready to work this problem.
    You need a good review of beginning algebra.
    This material should have been learned in middle school.
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  9. #9
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    Re: Complex equations

    Could you explain what the answer will be then just so I can understand?
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  10. #10
    MHF Contributor Reckoner's Avatar
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    ??? Still don't get it,sorry...
    This is a system of linear equations. You definitely should have learned how to solve these in an earlier algebra class.

    We have

    \begin{array}{rcrcr}x & + & 4y & = & 3\\-4x & + & y & = & 1\end{array}

    Multiply the first equation by 4:

    \begin{array}{rcrcr}4x & + & 16y & = & 12\\-4x & + & y & = & 1\end{array}

    Add the first equation to the second:

    \begin{array}{rcrcr}4x & + & 16y & = & 12\\&& 17y & = & 13\end{array}

    So y = \frac{13}{17}. Substitute this into the first equation and solve for x.

    Quote Originally Posted by Aiyla View Post
    Write the complex number z in polar form and the form eZ. Reply to this in precise form.
    z=2+2i
    Start by finding the modulus and argument of z. Consult your textbook if necessary.
    Thanks from Aiyla
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  11. #11
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    Could you explain what the answer will be then just so I can understand?
    This is not a tutorial service.
    You can find tutorial services in the web, but be prepared to pay.
    We are a free help service. But helping is different from tutoring.
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  12. #12
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    Re: Complex equations

    x= -1/17

    There, thx for the help!
    Last edited by Aiyla; June 6th 2012 at 03:26 PM.
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  13. #13
    MHF Contributor Reckoner's Avatar
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    Re: Complex equations

    Quote Originally Posted by Aiyla View Post
    x= -1/17
    Right. So then what does z equal?
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