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

Options

A. 6
B. 7
C. 8
D. none of these

Answer

B

Explanation

We have,
`z^(15)=1`
`rArr z=1^(1//15)`
`rArr z=e^(i2rpi//15),r=0,1,2,……14 [1^(1//n)=(e^(i2rpi)/n),r=0,1,….,(n-1)]`
`rArr z=e^(+-(i2pi)/15),r=0,1,2,……,7`
Thus, the complex numbers having their arguments between `-pi/2` and `pi/2` are:
`e^(0)=1, (e^(+-(i2pi)/15)), (e^(+-(i4pi)/15)), e^(+-(i6pi)/15)`
Clearly, the total number of these complex numbers is 7.