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anonymous

  • 4 years ago

10. find the 4th roots of the complex number z1=1+sqrt3+i part1: write z1 in polar form part2: find the mudulus of the root of z1 part3: find the four angles that define the 4th roots of the number z1 part4: what are the fourth roots of z1=sqrt3+i

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  1. EarthCitizen
    • 4 years ago
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    \[z ^{4}=(1+\sqrt{3})+i\] is this the correct expression ?

  2. anonymous
    • 4 years ago
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    its acually z with a 1 at the bottom, and everything else is correct

  3. EarthCitizen
    • 4 years ago
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    \[z _{1}=2.9<69.67^{o}\]

  4. anonymous
    • 4 years ago
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    thats in polar form?

  5. EarthCitizen
    • 4 years ago
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    yep

  6. anonymous
    • 4 years ago
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    you know how to find the muduus

  7. EarthCitizen
    • 4 years ago
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    yh, the modulus is just adding and squaring the x and y components to find the square root of the two

  8. EarthCitizen
    • 4 years ago
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    the \[|z _{1}|=2.9\]

  9. anonymous
    • 4 years ago
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    ok part3 and 4?

  10. EarthCitizen
    • 4 years ago
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    yh, what's the power of z ? it should be 4 ryt, since they need four roots ?

  11. anonymous
    • 4 years ago
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    and part4

  12. EarthCitizen
    • 4 years ago
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    1.3<17.42, 1.3<107.42, 1.3<197.42 and 1.3<287.42

  13. EarthCitizen
    • 4 years ago
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    the correct angles are 17.42,107.42, 197.42 and 287.42

  14. EarthCitizen
    • 4 years ago
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    part 4. \[z _{1}=\sqrt{3}+i\]

  15. EarthCitizen
    • 4 years ago
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    \[z _{1}= 2<30^{o}\] fourth roots in polar form 0.5<7.5, 0.5<97.5, 0.5<187.5 and 0.5<277.5

  16. EarthCitizen
    • 4 years ago
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    to convert to rectangular form, use de Moivre's theorem, \[r=[\cos(\theta)+isin(\theta)]\]

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