Finding the False Equation
Source:
March 8, 2009
trigonometry
Problem Statement
If x \equal{} \frac { \minus{} 1 \plus{} i\sqrt3}{2}\qquad\text{and}\qquad y \equal{} \frac { \minus{} 1 \minus{} i\sqrt3}{2}, where i^2 \equal{} \minus{} 1, then which of the following is not correct? (A)\ x^5 \plus{} y^5 \equal{} \minus{} 1 \qquad (B)\ x^7 \plus{} y^7 \equal{} \minus{} 1 \qquad (C)\ x^9 \plus{} y^9 \equal{} \minus{} 1
(D)\ x^{11} \plus{} y^{11} \equal{} \minus{} 1 \qquad (E)\ x^{13} \plus{} y^{13} \equal{} \minus{} 1