Show that the complex number z, satisfying the condition arg `((z -1)/(z + 1))=(pi)/(4) lies on a circle.

The locus of the points z satisfying the condition arg ((z-1)/(z+1))=pi/3 is, a

Show that the complex number z , satisfying are (z-1)/(z+1)=pi/4 lies on a circle.

For the complex number z satisfying the condition |z+(2)/(z)|=2 , the maximum value of |z| is

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

Find the locus of the complex number z=x+iy , satisfying relations arg(z-1)=(pi)/(4) and |z-2-3i|=2 .

The complex number which satisfies the condition |(i+z)/(i-z)|=1\ lies on a. circle \x^2+y^2=1 b. the x-axis c. the y-axis d. the line x+y=1

Find the locus of a complex number z such that arg ((z-2)/(z+2))= (pi)/(3)

Find the locus of a complex number z= x+ yi satisfying the relation arg (z-a)=(pi)/(4), a in R Illustrate the locus of z in the Argand plane

If the complex number z=x+i y satisfies the condition |z+1|=1, then z lies on (a)x axis (b) circle with centre (-1,0) and radius 1 (c)y-axis (d) none of these

For a non-zero complex number z , let arg(z) denote the principal argument with -pi lt arg(z)leq pi Then, which of the following statement(s) is (are) FALSE? arg(-1,-i)=pi/4, where i=sqrt(-1) (b) The function f: R->(-pi, pi], defined by f(t)=arg(-1+it) for all t in R , is continuous at all points of RR , where i=sqrt(-1) (c) For any two non-zero complex numbers z_1 and z_2 , arg((z_1)/(z_2))-arg(z_1)+arg(z_2) is an integer multiple of 2pi (d) For any three given distinct complex numbers z_1 , z_2 and z_3 , the locus of the point z satisfying the condition arg(((z-z_1)(z_2-z_3))/((z-z_3)(z_2-z_1)))=pi , lies on a straight line