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

If z=(1+7i)/((2-i)^2) , then find |z|?

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-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is

Complex numbers z satisfy the equaiton |z-(4//z)|=2 Locus of z if |z-z_(1)| = |z-z_(2)| , where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, is

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |(z_(1))/(z_(2))|= (|z_(1)|)/(|z_(2)|)

if z_(1) = 3i and z_(2) =1 + 2i , then find z_(1)z_(2) -z_(1)

If Real ((2z-1)/(z+1)) =1, then locus of z is , where z=x+iy and i=sqrt(-1)

If Real ((2z-1)/(z+1)) =1, then locus of z is , where z=x+iy and i=sqrt(-1)

Let f(z) is of the form alpha z +beta , where alpha, beta,z are complex numbers such that |alpha| ne |beta| .f(z) satisfies following properties : (i)If imaginary part of z is non zero, then f(z)+bar(f(z)) = f(barz)+ bar(f(z)) (ii)If real part of of z is zero , then f(z)+bar(f(z)) =0 (iii)If z is real , then bar(f(z)) f(z) gt (z+1)^2 AA z in R (4x^2)/((f(1)-f(-1))^2)+y^2/((f(0))^2)=1 , x , y in R , in (x,y) plane will represent :

If Z_(1)=2 + 3i and z_(2) = -1 + 2i then find (i) z_(1) +z_(2) (ii) z_(1) -z_(2) (iii) z_(1).z_(2) (iv) z_(1)/z_(2)