`arg(z_1z_2)=arg(z_1)+arg(z_2)`

Which of the following is correct for any tow complex numbers z_(1) and z_(2)?(a)|z_(1)z_(2)|=|z_(1)||z_(2)|(b)arg(z_(1)z_(2))=arg(z_(1))arg(z_(2))(c)|z_(1)+z_(2)|=|z_(1)|+|z_(2)|(d)|z_(1)+z_(2)|>=|z_(1)|+|z_(2)|

For any two complex numbers z1 and z2 ,prove that arg(z1.z2)=arg(z1)+arg(z2) .

arg(z_(1)z_(2))=arg(z_(1))+arg(z_(2))

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)

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

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

arg((z_(1))/(z_(2)))=arg(z_(1))-arg(z_(2))

If for complex numbers z_(1) and z_(2),arg(z_(1))-arg(z_(2))=0 then |z_(1)-z_(2)| is equal to

If for complex numbers z_1 and z_2 , arg(z_1) - arg(z_2)=0 , then show that |z_1-z_2| = | |z_1|-|z_2| |