Complex Numbers: $1-z+z^2-z^3=0$

Question

How to solve this equation? ($z$ is a complex number)

$1-z+z^2-z^3=0$

I tried using $z=a+ib$ and reached an answer but I'm not sure if it's a correct one.

Thanks!

I happen to see that $z=1$ is a solution...What do you think you can do with that? — imranfat, Nov 25 '15 at 16:40
If you think that you have an answer then you should be able to check it by plugging it in to the original equation — Andy, Nov 25 '15 at 16:40

score 4 · Answer 1 · answered Nov 25 '15 at 16:42

4

$$1-z+z^2-z^3=(1-z)(1+z^2)=0$$ $$z=1,\pm i$$

answered Nov 25 '15 at 16:42

Kay K.

score 0 · Answer 2 · answered Nov 25 '15 at 16:47

0

$1-z+z^2-z^3=0 $ is equivalent to $(1-z)(1+z^2)=0$,

then $(1-z)(i-z)(i+z)=0$. So, the solutions are:

$z=1$, $z=i$ or $z=-i$

answered Nov 25 '15 at 16:47

hachemy

2 Answers2