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 f(z)=(7-z)/(1-z^(2)), where z=1+2 i, then |f(z)| is

If f(z)=(7-z)/(1-z^(2)) where z=1+2i , the |f(z)| is equal to

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (d) None of these

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (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 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 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)=2 + 7i and z_(2)=1- 5i , then verify that |(z_(1))/(z_(2))|= (|z_(1)|)/(|z_(2)|)

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