Illustrate in the complex plane, the set of points satisfying the following condition. Explain your answer
arg `(z-2) = (pi)/(3)`

Illustrate in the complex plane, the set of points satisfying the following condition. Explain your answer |z| le 3

Illustrate in the complex plane, the set of points satisfying the following condition. Explain your answer |i-1-2z| gt 9

Illustrate in the complex plane the set of points z satisfying |z + i- 2| le 2

Illustrate in the complex plane the following set of points and explain your answer |Z|=3

Illustrate in the complex plane the following set of points and explain your answer arg (Z) = (pi)/(6)

Illustrate in the complex plane the following set of points and explain your answer |z| lt 5

Illustrate in the complex plane the following set of points and explain your answer |z-4| lt 1

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

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

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