What is locus of `z` if `|z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-pi/2|=1?`

What is the locus of z if |z-cos^(-1)cos12|-|z-sin^(-1)sin12||=8(pi-3)?

What is the locus of w if w=(3)/(z) and |z-1|=1?

Find the locus of z if arg ((z-1)/(z+1))= pi/4

The angle between the lines (x-1)/1=(y-1)/1=(z-1)/2a n d(x-1)/(-sqrt(3)-1)=(y-1)/(sqrt(3)-1)=(z-1)/4 is cos^(-1)(1/(65)) b. pi/6 c. pi/3 d. pi/4

If sin^(-1)x +cos^(-1)y +sin^(-1)z=2pi then 2x-z+y is :