Question

Complex numbers: how do i solve the complex equation: z^3 + z1*z = 0, where z1 = sqrt(3) + i?

Answer 1

z1= 2e^(ipi/6)
z(z^2 + z1)=0
z=0 or z = root(-z1)
z=0 or z=ie^(ipi/12)

Answer 2

sorry its 0 or 1.414ie^(ipi/12)

Answer 3

think there should be three solutions since polynomial has degree 3

Answer 4

the second soln has a + and -

Answer 5

\[z(z^2+(\sqrt{3}+i))=o\]
\[z=0\] or \[ z=\pm \sqrt{-\sqrt{3}-i}\]

Answer 6

\[-\sqrt{3}-i=2[cos(\frac{7\pi}{6})+i sin(\frac{7\pi}{6})]=2e^{\frac{7\pi}{6}i}\]
unless i made a mistake somewhere.

Answer 7

ur right

Answer 8

ok so root is \[\sqrt{2}e^{\frac{7\pi}{12}}\]

Answer 9

or \[\sqrt{2}e^{\frac{19\pi}{12}}\]