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Find the value of (cos pi/10+isin pi/10)*(cos 2pi/10+isin 2pi/10)*(cos 3pi/10+isin 3pi/10)*(cos 4pi/10+isin 4pi/10).

Find the value of (cos pi/10+isin pi/10)*(cos 2pi/10+isin 2pi/10)*(cos 3pi/10+isin 3pi/10)*(cos 4pi/10+isin 4pi/10).

Grade:11

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Arnab,

 

The terms in the first bracket is eiΠ/10, similarly others are

ei(2Π/10), ei(3Π/10), ei(4Π/10)

 

So the product is ei(1+2+3+4)Π/10 = e = cosΠ + isinΠ = -1+i(0) = -1.

 

Hence -1 is the answer.

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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