Let z be any non zero complex number, then find arg(z) + arg(z)

If z_(1) and z_(2) are non -zero complex numbers, then show that (z_(1) z_(2))^(-1)=z_(1)^(-1) z_(2)^(-1)

Let (z, w) be two non-zero complex numbers. If z +i w = 0 and arg (z w) = pi , then arg z is equal to a) pi b) (pi)/(2) c) (pi)/(4) d) (pi)/(6)

If x, y, z are non zero real numbers, then find the inverse of matrix A=[[x, 0, 0],[ 0, y, 0],[ 0, 0, z]] .

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1)| + |z_(2)| , then arg ((z_(1))/(z_(2))) is equal to a)0 b) -pi c) -(pi)/(2) d) (pi)/(2)

If z ^(2) + z + 1 = 0, where z is a complex number, then the value of (z + (1)/(z)) ^(2) + (z ^(2) + (1)/( z ^(2))) ^(2) + (z ^(3) + (1)/(z ^(3))) ^(2) +...( z ^(6) + (1)/(z ^(6)) )^(2) is

If z is a complex number with absz=2 and arg(z)=(4pi)/3 . then Find overline z