`arg((z-2)/(z+2))=pi/4`, Find the minimum value of `abs(z-9sqrt2-2i)^2`

A point z moves in the complex plane such that art (z-2)/(z+2)=(pi)/(4) then the minimum value of |z-9sqrt(2)-2i|^(2) is equal to ____________

If arg((z-2)/(z+2))=(pi)/(4) then the locus of z is

If arg(z_(1))=(2pi)/3 and arg(z_(2))=pi/2 , then find the principal value of arg(z_(1)z_(2)) and also find the quardrant of z_(1)z_(2) .

If arg((z_(1))/(z_(2)))=(pi)/(2), then find the value of |(z_(1)+z_(2))/(z_(1)-z_(2))|

If z lies on the curve arg (z+i)=(pi)/(4) , then the minimum value of |z+4-3i|+|z-4+3i| is [Note :i^(2)=-1 ]

If z is any complex number satisfying abs(z-3-2i) le 2 , where i=sqrt(-1) , then the minimum value of abs(2z-6+5i) , is

If z lies on the Curve (arg(z+i)=(pi)/(4)) then the minimum value of |z+4-3i|+|z-4+3i| is (Note i^(2)=-1 )

If z=x+iy and arg((z-2)/(z+2))=(pi)/(6), then find the locus of z.

If arg (z_(1))=(17pi)/18 and arg (z_(2))=(7pi)/18, find the principal argument of z_(1)z_(2) and (z_(1)//z_(2)).