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a ,b ,c are three complex numbers on the...

`a ,b ,c` are three complex numbers on the unit circle `|z|=1,` such that `a b c=a+b+c dot` Then find the value of `|a b+b c+c a|dot`

A

`3`

B

`6`

C

`1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `abara=bbarb=cbarc=1`
`:.bara=(1)/(a)` etc.
Now, `|abc|=|a+b+c|`
`=|bara+barb+barc|`
`=|(1)/(a)+(1)/(b)+(1)/(c )|`
`=|(sumab)/(abc)|`
`:.|sumab|=|abc||abc|=(|a||b||c|)^(2)=1`
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