# Math Help - compex numbers

1. ## compex numbers

solve

X to the power 15 + 1/ X to the power 25

when X + 1/X = 1

2. Originally Posted by sktulika
solve
X 15 +1/X 25

If X + 1/X =1
Does X 15 mean 15 X or X^15 .....? Does 1/X 25 mean 1/X^25, 1/(25 X) or 25/X .....?

Much greater clarity is required.

3. Originally Posted by mr fantastic
Does X 15 mean 15 X or X^15 .....? Does 1/X 25 mean 1/X^25, 1/(25 X) or 25/X .....?

Much greater clarity is required.
So you want to find the value of $x^{15} + \frac{1}{x^{25}}$ given that $x + \frac{1}{x} = 1$.

A brutal approach:

$x + \frac{1}{x} = 1 \Rightarrow x^2 - x + 1 = 0 \Rightarrow x = ......$. Express the solution in polar form.

$x^{15} + \frac{1}{x^{25}} = \frac{1}{x^{25}} (x^{40} + 1)$. Substitute the polar form of x, use de Moivre's theorem and tidy up.