## anonymous 5 years ago Complex numbers: how do i solve the complex equation: z^3 + z1*z = 0, where z1 = sqrt(3) + i?

1. anonymous

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

2. anonymous

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

3. anonymous

think there should be three solutions since polynomial has degree 3

4. anonymous

the second soln has a + and -

5. anonymous

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

6. 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.

7. anonymous

ur right

8. anonymous

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

9. anonymous

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