(1 3w+w^2)(1+w 3w^2) we know that , 1+w+w^2=0 , w^3=1 = ( w 3w)( w^2 3w^2) =(4w)(4w^2) #160; =16w^3 =16 ...

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Cube Root of a Complex Number

Simplify: 1...

Question

Simplify: $(1 - 3 ω + ω^{2}) (1 + ω - 3 ω^{2})$

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Solution

$(1 - 3 w + w^{2}) (1 + w - 3 w^{2})$

we know that ,

$1 + w + w^{2} = 0$ , $w^{3} = 1$

$= - (- w - 3 w) (- w^{2} - 3 w^{2})$

$= (4 w) (4 w^{2})$

$= 16 w^{3}$

$= 16$

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