Identify the locus of `z` if ` bar z = bar a +(r^2)/(z-a).`

Solve for z: bar (z) = iz ^ (2)

Let z=x+iy. Then find the locus of P(z) such that (1+bar(z))/(z)in R

Let z=x+iy then locus of moving point P(z)(1+bar(z))/(z)in R, is

If z=i-1, then bar(z)=

arg(bar(z))=-arg(z)

Let I Arg((z-8i)/(z+6))=pmpi/2 II: Re ((z-8i)/(z+6))=0 Show that locus of z in I or II lies on x^2+y^2+6^x – 8^y=0 Hence show that locus of z can also be represented by (z-8i)/(z+6)+(bar(z)-8i)/(barz+6)=0 Further if locus of z is expressed as |z + 3 – 4i| = R, then find R.

If arg(z)=-(pi)/(4) then the value of arg((z^(5)+(bar(z))^(5))/(1+z(bar(z))))^(n) is