If the argument of (z-a)(barz-b) is equa...

If the argument of `(z-a)(barz-b)` is equal to that `((sqrt(3)+i)(1+sqrt(3)i))/(1+i)` where a,b, are two real number and z is the complex conjugate of the complex number z find the locus of z in the Argand diagram. Find the value of a and b so that locus becomes a circle having its centre at `1/2(3+i)`

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