Complex Numers

VITEEE 2015 Coaching › Co-ordinate Geometry questions › Complex Numers

Evaluate Î£_p=1³² (3p+2)[Î£_q=1¹⁰{sin(2qÎ /11)- icos(2qÎ /11)]^p

#Mathematics #Co-ordinate Geometry

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5 Answers

106

Asish Mahapatra ·2009-12-08 02:15:01

could you latexify that please.. unable to understand that last ^p

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Nikhil Kaushik ·2009-12-08 03:19:54

that is the power of the internal summation.....

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106

Asish Mahapatra ·2009-12-08 03:28:22

ok. then

\sum_{q=1}^{10}{sin(2q\pi /11)-icos(2q\pi /11)}

=-i\sum_{q=1}^{10}{cos(2q\pi /11)+isin(2q\pi /11)}

= i

So the sum is =\sum_{p=1}^{32}{(3p+2)i^p}=\sum_{p=1}^{32}{(3p)i^p}

= 3i(1-3+5-7+9-11+...-31) + 3(-2+4-6+8-10+12-...+32)
= 3i(-16) + 3(16)
= 48(1-i)

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Nikhil Kaushik ·2009-12-08 03:35:47

you made a silly mistake...........the real part should be +ve........the correct answer is 48(1-i).
Check your the IIIrd last step again.....

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106

Asish Mahapatra ·2009-12-08 03:37:24

yes.. was in a hurry edited

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Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

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