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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:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student,
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
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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