Question

(1+ alpha ) (1+beta)(1+alpha sq.))1+beta sq.) = 1

prove it.

Answer 1

Answer:

Chapter Name : Complex Numbers

($(1+\alpha )(1+\beta )(1+\alpha ^{2} )(1+\beta^{2}  )$

take \alpha = ω

       \beta = ω^{2}

Now , as per to the question,

(1+ω)(1+ω^{2})(1+ω^{2})(1+ω^4)

=> (-ω^{2})(-ω)(-ω)(1+ω)

=> ω^{3}(-ω)(-ω^{2})

=>  ω^{3}.ω^{3}

=> 1*1

=> 1

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Formula used : 1+ ω+ ω^{2} = 0

(1+ω) = -ω^2

(1+ω^2) = -ω

ω^{3} = 0

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hope it helps :)

thanks:)