anonymous
  • anonymous
Complex numbers: how do i solve the complex equation: z^3 + z1*z = 0, where z1 = sqrt(3) + i?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
z1= 2e^(ipi/6) z(z^2 + z1)=0 z=0 or z = root(-z1) z=0 or z=ie^(ipi/12)
anonymous
  • anonymous
sorry its 0 or 1.414ie^(ipi/12)
anonymous
  • anonymous
think there should be three solutions since polynomial has degree 3

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anonymous
  • anonymous
the second soln has a + and -
anonymous
  • anonymous
\[z(z^2+(\sqrt{3}+i))=o\] \[z=0\] or \[ z=\pm \sqrt{-\sqrt{3}-i}\]
anonymous
  • anonymous
\[-\sqrt{3}-i=2[cos(\frac{7\pi}{6})+i sin(\frac{7\pi}{6})]=2e^{\frac{7\pi}{6}i}\] unless i made a mistake somewhere.
anonymous
  • anonymous
ur right
anonymous
  • anonymous
ok so root is \[\sqrt{2}e^{\frac{7\pi}{12}}\]
anonymous
  • anonymous
or \[\sqrt{2}e^{\frac{19\pi}{12}}\]

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