If `arg z = alpha` and |z-1|= 1 then `|(z-2)/z|` is equal to

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If |z-1| =1 and arg (z)=theta , where z ne 0 and theta is acute, then (1-2/z) is equal to

If |z-1| =1 and arg (z)=theta , where z ne 0 and theta is acute, then (1-2/z) is equal to

If arg ((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3 , then |z_(1)| equals to

If arg ((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3 , then |z_(1)| equals to

If arg(z) lt 0 , then arg(-z)-arg(z) is equal to

If for complex numbers z_(1) and z_(2) , arg z_(1)-"arg"(z_(2))=0 then |z_(1)-z_(2)| is equal to

If z_(1),z_(2) and z_(3) are three distinct complex numbers such that |z_(1)| = 1, |z_(2)| = 2, |z_(3)| = 4, arg(z_(2)) = arg(z_(1)) - pi, arg(z_(3)) = arg(z_(1)) + pi//2 , then z_(2)z_(3) is equal to