Question

${w}^{7} + {w}^{14} =$
a) 0
b) 1
c)-1
d)3
Explain with detail ;​

Answer 1

✣ Answer ✣

Note - I am assuming that here ω is cube root of unity as it is not specified.

Formulas required -

• 1 + ω + ω²  = 0

• ω³  = 1

Process-

ω⁷ + ω¹⁴ = ω x ω⁶ + ω² x ω¹² = ω x 1² + ω² x 1⁴

= ω + ω²

Now, add and subtract 1. We get:

1 + ω + ω² -1

Now, as formula, we know that 1 + ω + ω² = 0.

So,

1 + ω + ω² - 1 = 0 - 1 = -1