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1.What is Fibonacci series
2.What is the cube root of unity

Asked by rbhatt16 12th October 2017, 5:16 PM
Answered by Expert
Answer:
begin mathsize 16px style Fibonacci space Sequence space is space the space sequence space such space that space next space number space is space always
sum space of space the space two space numbers space before space it.

For space example colon
0 comma space 1 comma space 1 comma space 2 comma space 3 comma space 5 comma space 8 comma...........
Here comma space first space term space is space 0.
second space term space is space 1 space plus space 1 space equals space 2
Third space term space is space 1 space plus space 2 space equals space 3
and space so space on..........



Complex space numbers space are space in space the space form space of space straight a thin space plus thin space bi
where space straight a space is space real space part space and space straight b space is space the space imaginary space part.
Complex space cube space root space of space unity space means comma
straight x cubed space equals space 1
rightwards double arrow straight x cubed space minus space 1 space equals space 0
rightwards double arrow open parentheses straight x minus 1 close parentheses open parentheses straight x squared plus straight x plus 1 close parentheses equals 0
rightwards double arrow straight x minus 1 space equals space 0 space or space straight x squared plus straight x plus 1 space equals space 0
straight x space equals space 1 space or space straight x squared plus straight x plus 1 space equals space 0
Consider comma
straight x squared plus straight x plus 1 space equals space 0
If space we space solve space it space by space quadratic space equations space using space formula space we space get
straight x space equals space fraction numerator negative 1 space plus-or-minus space square root of 1 minus 4 cross times 1 cross times 1 end root over denominator 2 end fraction
straight x space equals space fraction numerator negative 1 space plus-or-minus space square root of negative 3 end root over denominator 2 end fraction
straight x space equals fraction numerator negative 1 space plus-or-minus space square root of 3 space straight i over denominator 2 end fraction space space space space space space space where space square root of negative 1 end root space equals space straight i end style
Answered by Expert 21st December 2017, 2:51 PM
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