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STD 11 - 4.1 complex nubers — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 4.1 complex nubers1 Mark
MCQ
If $\omega $ is a complex cube root of unity, then $(x - y)(x\omega - y)$ $(x{\omega ^2} - y) = $
  • A
    ${x^2} + {y^2}$
  • B
    ${x^2} - {y^2}$
  • ✓
    ${x^3} - {y^3}$
  • D
    ${x^3} + {y^3}$
✓

Answer

Correct option: C.
${x^3} - {y^3}$
c
(c)$(x - y)(x\omega - y)(x{\omega ^2} - y)$
$ = ({x^2}\omega - xy - xy\omega + {y^2})(x{\omega ^2} - y)$
$ = {x^3} - {x^2}y(1 + \omega + {\omega ^2}) + x{y^2}(1 + \omega + {\omega ^2}) - {y^3}$
$ = {x^3} - {y^3}$

$(\because 1 + \omega  + {\omega ^2} = 0)$

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