Let $z_1 = k + 1 + i(k − 1)$ and $z_2 = 2k − ik$ be to complex numbers, whats the value for $k$ if...











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Let $z_1 = k + 1 + i(k − 1)$ and $z_2 = 2k − ik$ be to complex numbers, whats the value for $k$ if $dfrac{z_1}{z_2} $is real number?




Answer is $dfrac13$, but I don't know how to solve it.






calculus analysis







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  • just set imaginary part to zero
    – phdmba7of12
    yesterday















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Let $z_1 = k + 1 + i(k − 1)$ and $z_2 = 2k − ik$ be to complex numbers, whats the value for $k$ if $dfrac{z_1}{z_2} $is real number?




Answer is $dfrac13$, but I don't know how to solve it.






calculus analysis







share|cite|improve this question









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Nadja is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • just set imaginary part to zero
    – phdmba7of12
    yesterday













up vote
0
down vote

favorite









up vote
0
down vote

favorite












Let $z_1 = k + 1 + i(k − 1)$ and $z_2 = 2k − ik$ be to complex numbers, whats the value for $k$ if $dfrac{z_1}{z_2} $is real number?




Answer is $dfrac13$, but I don't know how to solve it.






calculus analysis







share|cite|improve this question









New contributor




Nadja is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












Let $z_1 = k + 1 + i(k − 1)$ and $z_2 = 2k − ik$ be to complex numbers, whats the value for $k$ if $dfrac{z_1}{z_2} $is real number?




Answer is $dfrac13$, but I don't know how to solve it.






calculus analysis




calculus analysis






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Nadja is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited yesterday









Tianlalu

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2,589632






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asked yesterday









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  • just set imaginary part to zero
    – phdmba7of12
    yesterday


















  • just set imaginary part to zero
    – phdmba7of12
    yesterday
















just set imaginary part to zero
– phdmba7of12
yesterday




just set imaginary part to zero
– phdmba7of12
yesterday










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HINT: Note that $frac{z_1}{z_2}=frac{z_1overline{z_2}}{|z_2|^2}$, and in the latter the denominator is a real number (if $k$ is real).






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    HINT: Note that $frac{z_1}{z_2}=frac{z_1overline{z_2}}{|z_2|^2}$, and in the latter the denominator is a real number (if $k$ is real).






    share|cite|improve this answer

























      up vote
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      HINT: Note that $frac{z_1}{z_2}=frac{z_1overline{z_2}}{|z_2|^2}$, and in the latter the denominator is a real number (if $k$ is real).






      share|cite|improve this answer























        up vote
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        up vote
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        down vote









        HINT: Note that $frac{z_1}{z_2}=frac{z_1overline{z_2}}{|z_2|^2}$, and in the latter the denominator is a real number (if $k$ is real).






        share|cite|improve this answer












        HINT: Note that $frac{z_1}{z_2}=frac{z_1overline{z_2}}{|z_2|^2}$, and in the latter the denominator is a real number (if $k$ is real).







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        answered yesterday









        Servaes

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