Question

Value of w30 + w21 is………, where w is complex cube root of unity

Answer 1

Answer:

The value of ω³⁰ + ω²¹ is ω + 1

Step-by-step explanation:

Given ω³⁰ + ω²¹

Taking common from both the terms, we get

ω²¹ ( ω⁷ + 1 )

We know that ω³ = 1

Therefore ω²¹ = ω³*⁷ (ω³)⁷ = (1)⁷ = 1

         and  ω⁷ = ω⁶⁺¹ = ω⁽³*²⁾⁺¹ = (ω³)² . ω¹ = (1)² .ω = 1. ω = ω

Therefore ω²¹ ( ω⁷ + 1 ) = 1( ω + 1)

                                      = ω + 1

Therefore, the value of ω³⁰ + ω²¹ is ω + 1