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Home / Doubts and Solutions/ICSE/Class 11 Science/Mathematics

solve it with iota and omega

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Asked by defence 24th April 2019, 11:57 AM
Answered by Expert
Answer:
omega space i s space a n space i m a g i n a r y space c u b e space r o o t space o f space u n i t y rightwards double arrow omega cubed equals 1 rightwards double arrow omega cubed minus 1 equals 0 rightwards double arrow left parenthesis omega minus 1 right parenthesis left parenthesis omega squared plus omega plus 1 right parenthesis equals 0 space.... space u sin g space t h e space f o r m u l a space o f space c u b e s space o f space b i n o m i a l s S i n c e comma space omega not equal to 1 space rightwards double arrow omega squared plus omega plus 1 equals 0 space...... space left parenthesis i right parenthesis T o space p r o v e colon space fraction numerator 1 over denominator 1 plus 2 omega end fraction plus fraction numerator 1 over denominator 2 plus omega end fraction minus fraction numerator 1 over denominator 1 plus omega end fraction equals 0 L H S equals fraction numerator 1 over denominator 1 plus 2 omega end fraction plus fraction numerator 1 over denominator 2 plus omega end fraction minus fraction numerator 1 over denominator 1 plus omega end fraction equals fraction numerator left parenthesis 2 plus omega right parenthesis left parenthesis 1 plus omega right parenthesis plus left parenthesis 1 plus 2 omega right parenthesis left parenthesis 1 plus omega right parenthesis minus left parenthesis 1 plus 2 omega right parenthesis left parenthesis 2 plus omega right parenthesis over denominator left parenthesis 1 plus 2 omega right parenthesis left parenthesis 2 plus omega right parenthesis left parenthesis 1 plus omega right parenthesis end fraction equals fraction numerator 2 plus 3 omega plus omega squared plus 1 plus 3 omega plus 2 omega squared minus 2 minus 5 omega minus 2 omega squared over denominator left parenthesis 1 plus 2 omega right parenthesis left parenthesis 2 plus omega right parenthesis left parenthesis 1 plus omega end fraction equals fraction numerator 3 plus 6 omega plus 3 omega squared minus 2 minus 5 omega minus 2 omega squared over denominator left parenthesis 1 plus 2 omega right parenthesis left parenthesis 2 plus omega right parenthesis left parenthesis 1 plus omega right parenthesis end fraction equals fraction numerator 1 plus omega plus omega squared over denominator left parenthesis 1 plus 2 omega right parenthesis left parenthesis 2 plus omega right parenthesis left parenthesis 1 plus omega right parenthesis end fraction equals 0 space.............. space U sin g space left parenthesis i right parenthesis H e n c e comma space fraction numerator 1 over denominator 1 plus 2 omega end fraction plus fraction numerator 1 over denominator 2 plus omega end fraction minus fraction numerator 1 over denominator 1 plus omega end fraction equals 0.
Answered by Expert 25th April 2019, 10:21 AM
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