If `f(z)=(7-z)/(1-z^2)` , where `z=1+2i ,` then `|f(z)|` is `(|z|)/2` (b) `|z|` (c) `2|z|` (d) none of these

If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (a)(|z|)/2 (b) |z| (c) 2|z| (d) none of these

If w=alpha+i beta, where beta!=0 and z!=1 satisfies the condition that ((w-wz)/(1-z)) is a purely real,then the set of values of z is |z|=1,z!=2( b) |z|=1 and z!=1z=z(d) None of these

If int(x^2-2)/((x^4+5x^2+4)tan^-1((x^2+2)/x))dx=log|f(z)|+c , then (A) f(z)=tan^-1z , where z=sqrt(x+2) (B) f(z)=tan^-1z , where z=x+2/x (C) f(z)=sin^-1z , where z=(x+2)/x (D) none of these

If |z|=1 and w=(z-1)/(z+1) (where z!=-1) then Re(w) is (A) 0(B)-(1)/(|z+1|^(2))(C)|(z)/(z+1)|(1)/(|z+1|^(2))(D)(sqrt(2))/(|z+1|^(2))

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

If z is a non zero complex,number then |(|z|^(2))/(zz) is equal to |(z)/(z)| b.|z| c.|z| d.none of these

If amp (z_(1)z_(2))=0 and |z_(1)|=|z_(2)|=1, then z_(1)+z_(2)=0 b.z_(1)z_(2)=1 c.z_(1)=z_(2)^(*) d.none of these

If z_(1),z_(2),z_(3) are three distinct non-zero complex numbers and a,b,c in R^(+) such that (a)/(|z_(1)-z_(3)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|),quad then (a^(2))/(z_(1)-z_(2))+(b^(2))/(z_(2)-z_(3))+(c^(2))/(z_(2)-z_(1)) is equal to Re(z_(1)+z_(2)+z_(3))( b) Im g(z_(1)+z_(2)+z_(3))0(d) None of these

Let A(z_1),B(z_2) and C(z_3) be the vertices of an equilateral triangle in the Argand plane such that |z_1|=|z_2|=|z_3|. Then (A) (z_2+z_3)/(2z_1-z_2-z_3) is purely real (B) (z_2-z_3)/(2z_1-z_2-z_3) is purely imaginary (C) |arg(z_1/z_2)|=2 arg((z_3-z_2)/(z_1-z_2))| (D) none of these