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from complex numbers. QUESTION: {1+Cos pi/8 + iSin pi/8}/ {1 + Cos pi/8 - iSin pi/8} whole raise to power 8 is equal to? please explain. thank you :)

from complex numbers.

QUESTION:
{1+Cos pi/8 + iSin pi/8}/ {1 + Cos pi/8 - iSin pi/8} whole raise to power 8 is equal to?

please explain.
thank you :)

Grade:12th pass

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
{1+cos pi/8 +isin pi/8}/{1+cos pi/8 -isin pi/8}
={2cos^pi/16+i2sinpi/16cospi/16}/2cos^2pi/16-i2sinpi/16cospi/16}
={2cospi/16(cospi/16+isinpi/16)}/{2cospi/16(cospi/16-isinpi/16)}
=e^ipi/16/e^-ipi/16=e^ipi/8
hence solution will be {e^ipi/8)^8=e^ipi=cospi+isinpi=-1
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
RAJAT CHHABRA
16 Points
8 years ago
wow! that was easy! wud have done that.! anyways thanks :)

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