anonymous
  • anonymous
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
Mathematics
katieb
  • katieb
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EarthCitizen
  • EarthCitizen
\[z ^{4}=(1+\sqrt{3})+i\] is this the correct expression ?
anonymous
  • anonymous
its acually z with a 1 at the bottom, and everything else is correct
EarthCitizen
  • EarthCitizen
\[z _{1}=2.9<69.67^{o}\]

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anonymous
  • anonymous
thats in polar form?
EarthCitizen
  • EarthCitizen
yep
anonymous
  • anonymous
you know how to find the muduus
EarthCitizen
  • EarthCitizen
yh, the modulus is just adding and squaring the x and y components to find the square root of the two
EarthCitizen
  • EarthCitizen
the \[|z _{1}|=2.9\]
anonymous
  • anonymous
ok part3 and 4?
EarthCitizen
  • EarthCitizen
yh, what's the power of z ? it should be 4 ryt, since they need four roots ?
anonymous
  • anonymous
and part4
EarthCitizen
  • EarthCitizen
1.3<17.42, 1.3<107.42, 1.3<197.42 and 1.3<287.42
EarthCitizen
  • EarthCitizen
the correct angles are 17.42,107.42, 197.42 and 287.42
EarthCitizen
  • EarthCitizen
part 4. \[z _{1}=\sqrt{3}+i\]
EarthCitizen
  • EarthCitizen
\[z _{1}= 2<30^{o}\] fourth roots in polar form 0.5<7.5, 0.5<97.5, 0.5<187.5 and 0.5<277.5
EarthCitizen
  • EarthCitizen
to convert to rectangular form, use de Moivre's theorem, \[r=[\cos(\theta)+isin(\theta)]\]

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