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Complex Numbers question

2009 · Shift 1 · Q22

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2009 · Shift 1 · Q22

Complex Numbers question

2009 · Shift 1 · Q22

JEE AdvancedMathematicsComplex NumbersMCQ+3 / −1

Let

z = \,\cos \,\theta \, + i\,\sin \,\theta

. Then the value of

\sum\limits_{m = 1}^{15} {{\mathop{\rm Im} olimits} } ({z^{2m - 1}})\,at\,\theta \, = {2^ \circ }

is

A
${1 \over {\sin \,{2^ \circ }}}$
B
${1 \over {3\sin \,{2^ \circ }}}$
C
${1 \over {2\sin \,{2^ \circ }}}$
D
${1 \over {4\sin \,{2^ \circ }}}$

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