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).

Hi Arnab,

The terms in the first bracket is e^iΠ/10, similarly others are

e^i(2Π/10), e^i(3Π/10), e^i(4Π/10)

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

Hence -1 is the answer.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).