Question

The cube roots of unity are: 1, ω = $\frac{-1 + i\sqrt{3} }{2}$ and ω² = $\frac{-1 - i\sqrt{3} }{2}$, where 1 is the real cube root of unity and ω, ω² are the complex cube roots of unity.

Properties:

* ω³ = 1

* 1 + ω + ω² = 0


Based on the above solve the following equation:

(1 - ω + ω²)⁷ + (1 + ω - ω²)⁷

a) 128

b) 64

c) 256

d) -128


Please answer correctly with no spam. If your answer is useful to me I will mark it as the brainliest.

Class 11 Mathematics

Answer 1

Answer:

SOLUTION

Correct option is

C

i3

Let w be the cube root of unity.

∴w3=1&1+w2+w=0

where, w=2−1+i3&w2=21−i3         ...(1)

z=4+5(2−1+i3)334+3(2−1+i3)365=4+5w334+3w365        ...{from (1)}

⟹z=4+5[(w3)111w]+3[(w3)121w2]=4+5w+3w2         ...{∵w3=1}

⟹

Answer 2

Answer:

correct option is c

Step-by-step explanation:

i hope you understand the answer