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Find the number of roots of the equati...

Find the number of roots of the equation `z^(15) = 1` satisfying `|arg z| lt pi//2`.

Text Solution

Verified by Experts

The correct Answer is:
7
We have `z^(15) = 1`
`z=1^(1)/(15) = e^(i(2rpi)/(15)), r = 0, 1,2,.....,14`
or `z =e^(pmi(2rpi)/(15)) , r=0,1,2,....7`
The complex numbers having their arguments between `-(pi)/(2)` and `(pi)/(2)` are `e^(0), e^(pmi(2pi)/(15)),e^(pmi(4pi)/(15)),e^(pmi(6pi)/(15))`.
Hence number of solutions is7.
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