Question

If \(a\) and \(b\) are the roots of \(x^2-2x+4=0\), then
\(a^9 +b^9 = ?\\
a^{10} + b^{10} = ?\)

Answer 1

you can use demoivre's theorem , if you change the complex roots to polar trig form

Answer 2

or exponential trig form

Answer 3

that works nicely!!!

Answer 4

It makes sense because of the \(\large \pm\) in the quadratic formula.

Answer 5

To me anyway. That logic could be completely wrong...but, idk

Answer 6

a,b=
x^2-2x-1+4=0
(x-1)^2=-3
x=+/- sqrt3 i + 1

\[a= 1+\sqrt3 i\\
b= 1-\sqrt3 i\]
polar form now