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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 `abc=a+b+c`. Then `|ab+bc+ca|` is equal to

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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