If $a = \cos {\rm{\alpha }} + i\sin {\rm{\alpha }},\;b = \cos {\rm{\beta }} + i\sin {\rm{\beta }},\;c = \cos {\rm{\gamma }} + i\sin {\rm{\gamma }}\;{\rm{and\;}}\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 1,\;$ then $\cos \left( {{\rm{\beta }} - {\rm{\gamma }}} \right) + \cos \left( {{\rm{\gamma }} - {\rm{\alpha }}} \right) + \cos \left( {{\rm{\alpha }} - {\rm{\beta }}} \right){\rm{\;}}$ is equal to

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

a = \cos \mathrm{\alpha } + i\sin \mathrm{\alpha },\;b = \cos \mathrm{\beta } + i\sin \mathrm{\beta },\;c = \cos \mathrm{\gamma } + i\sin \mathrm{\gamma }\;\mathrm{and\;}\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 1,\;

then

\cos \left( {\mathrm{\beta } - \mathrm{\gamma }} \right) + \cos \left( {\mathrm{\gamma } - \mathrm{\alpha }} \right) + \cos \left( {\mathrm{\alpha } - \mathrm{\beta }} \right)\mathrm{\;}

is equal to

View answer and explanation

Correct option: D

Option B (0) is correct because the product of the roots of the given function, as n approaches infinity, is 0.