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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+cdot` Then find the value of `|a b+b c+c a|dot`

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a, b, c are complex numbers on the unit circle `|z| = 1 `
` therefore |a| = |b| = |c| = 1 `
` therefore a bara = bbarb = cbarc = 1 `
` " " abc = a + b + c `
` rArr |abc| = |a + b + c | `
` " "= |bara + bar b + bar c | `
` " " = |(1)/(a) + (1)/(b) + (1)/(c ) | `
` " " = | (ab + bc + ca )/( abc ) | `
` therefore | ab + bc + ca | = |abc | |abc | = (|a| |b| |c|)^(2) = 1 `
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