Polynomial equation with complex numbers I'm studying linear algebra and there are a few problems from the book in the section on complex numbers I'm having trouble with. I've solved most of the questions in this chapter - I need a little help with these last five. Here's one of them - there are two statements and I have to answer true or false for each one.


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*If $z_0$ is a solution for the equation $z^{13}-13z^7+7z^3-3z+1=0$ then $\overline{z}_0$ is also a solution for it.

*if $z_0$ is a solution for the equation $z^2+iz+2=0$ then $\overline{z}_0$ is also a solution for it.
Can anyone help me out?

1 is true, by taking the conjugate of both sides of the equation, and then apply properties of conjugates.  
2 is false, since the coefficient of the z term is not real, it can be shown to be false by a similar method as in 1.
