SATHEE: Complex Numbers 5 Question 9

Complex Numbers 5 Question 9

10. If $ω$ is an imaginary cube root of unity, then ${(1 + ω - ω^{2})}^{7}$ is equal to

(a) $128 w$

(b) $- 128 ω$

(c) $128 ω^{2}$

(d) $- 128 ω^{2}$

(1998, 2M)

Show Answer

Answer:

Correct Answer: 10. (d)

Solution:

${(1 + ω - ω^{2})}^{7} = {(- ω^{2} - ω^{2})}^{7}$

$[∵ 1 + ω + ω^{2} = 0]$

$= {(- 2 ω^{2})}^{7} = (- 2)^{7} ω^{14} = - 128 ω^{2}$

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