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Math Help - Complex Complex

  1. #1
    Junior Member
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    Complex Complex

    if a is a complex number which satisfy ia^3+a^2-a+1=0

    then find \left | a \right |?

    one way is to put a=x+iy

    any other short way ?
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  2. #2
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    Hello, banku12!

    Is there a typo?
    If the last term is i, I can solve it.


    If a is a complex number which satisfies: . ia^3+a^2-a + {\color{red}i}\:=\:0

    then find: . |a|

    Divide by i\!:\;\;a^3 + \frac{a^2}{i} - \frac{a}{i} + \frac{i}{i} \:=\:0 \quad\Rightarrow\quad a^3 - ia^2 + ia + 1 \:=\:0


    \begin{array}{ccccc}\text{We have:} & a^3 - ia^2 + ia - i^2 &=& 0 \\ \\<br /> <br />
\text{Factor:} & a^2(a-i) + i(a-i) &=& 0 \\ \\<br /> <br />
\text{Factor:} & (a-i)(a^2+i) &=& 0 \end{array}

    . . Hence: . a \;=\;i,\;\pm\sqrt{i}


    Therefore, for all roots: . |a|\:=\:1

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  3. #3
    Junior Member
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    No..actually there is no typo..

    btw is it not possible to compute mod a if last term in the given exp is 1 ?
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