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## [SOLVED] Urgent help needed with complex numbers

1. The problem statement, all variables and given/known data
a complex no. z is represented by the point T in an Argand diagram.

$$z=\frac{1}{3+it}$$

where t is a variable

show that z+z*=6ZZ*

and that as t varies,T lies on a circle, and state its centre
2. Relevant equations

3. The attempt at a solution

Did the first part easily.

Need help with the 2nd part with the circle

so far I multiplied z by z*/z* to get

$$z=\frac{3-it}{p+t^2}$$

Do I now say that let z=x+iy and then find |z| and the modulus of the otherside (with t) and put that in the form $x^2+y^2+2fx+2gy+c=0$ ?