If `z=1+i`,then mention the value of `arg(z)`.

If sin^(-1) x +sin^(-1)y +sin^(-1) z =(3pi)/(2) , then find the value of x^(100) +y^(100) +z^(100) -(9)/(x^(101)+y^(101)+z^(101)) .

If z=(3+4i)/i ,then find |z|

If the lines (x -1)/(-3) = (y -2)/(2 lamda ) = ( z -3)/( 2) and ( x -1)/( 3 lamda ) = ( y-1)/(1) = ( z - 6)/( -5) are perpendicular to each other , what is the value of lamda ?

If the planes 2x - 4y + 3z = 5 and x + 2y + gamma z = 12 are perpendicular to each other, what is the value of lamda ?

If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?

If x, y, z are all positive real numbers, then prove that, If x+y+z=1 , then prove that (1-x)(1-y)(1-z)ge8xyz .

If z be a complex number, show that the minimum value of |z| + |z - 1| is 1.

In the series Sc(Z = 21) to Zn (Z =30), the enthalpy of atomization of zinc is the lowest i.e. 126 kJ mol^(-1) . Why?