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Z^4+1=0 has 4 distinct and non-zero solutions. HOW?

Z^4+1=0 has 4 distinct and non-zero solutions.
HOW?

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
z^4+1=0
z^4=-1=cospi+isinpi
z^4=cos(2npi+pi)+isin(2npi+pi)
z^4=cos(2n+1)pi +i sin(2n+1)pi=e^i(2n+1)pi
z=e^i(2n+1)pi/4
z=e^ipi/4, e^i(3pi/4) , e^i(5pi/4) ,e^i(7pi/4)

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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