The equation `az^(3) + bz^(2) + barbz + bara = 0` has a root `alpha`, where a, b,z and `alpha` belong to the set of complex numbers. The number value of `|alpha|`

Options

A. is 1/2
B. is 1
C. is 2
D. can't be determined

Answer

B

Explanation

We have `az^(3)+bz^(2)+barbz+bar a =0" "…(1)`
Taking conjugate of both sides, we get
`rArr barabarz^(3)+barb barz^(2)+b barz+a=0`
Dividing this equation by `barz^(3)`and writing the terms in reverse order, we get
`(a)/(barz^(3))+(b)/(barz^(2))+(barb)/(barz)+bara=0 " "["For "barzne0]" "...(2)`
Since equations (1) and (2) are identical.
`z^(3)=(1)/(barz^(3))rArr|z\|^(6)=1 rArr|z|=1`
Therefore, if `alpha` is a root of the given equation, then `|alpha|=1`.