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Question
I need to solve the equation
z to the 5 = i
Please help!
Hello Terry,
z^5=i=1*e^(i*T), where T=pi/2...using DeMoivre's Thrm...
z=1^(1/5)[cos(T/5)+i*sin(T/5)]
or 1^(1/5)[cos((T+2pi)/5)+i*sin((T+2pi)/5)]
or 1^(1/5)[cos((T+4pi)/5)+i*sin((T+4pi)/5)]
or 1^(1/5)[cos((T+6pi)/5)+i*sin((T+6pi)/5)]
or 1^(1/5)[cos((T+8pi)/5)+i*sin((T+8pi)/5)]
OK? Can you finish it from here?
TTYL, Abe
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Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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