Write the value of `a r g(z)+a r g( z conjugate )` .

For a complex number z=x+ iy find the modulus of zbar(z) where bar(z) is the conjugate of z

Write the value of Delta = |(x+y, y +z , z +x),(z, x,y),(-3,-3,-3)|

If z_(1),z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, the find the value of arg(z_(1)/z_(4)) + arg(z_(2)//z_(3)) .

If f:R -> R, g:R -> R defined as f(x) = sin x and g(x) = x^2 , then find the value of (gof)(x) and (fog)(x) and also prove that gof != fog .

If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies in the interval (a in R)

The maximum value of |ar g(1/(1-z))| for |z|=1 ,z!=1 is given by

For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - sqrt(2pi t) + 3pi The value of x + y + z is equal to

For the reaction at 300 K A(g)hArrV(g)+S(g) Delta_(r)H^(@)=- 30 kJ//mol, Delta_(r)S^(@)=-0.1K^(-1).mol^(-1) What is the value of equilibrium constant ?

If P(z_(1)),Q(z_(2)),R(z_(3)) " and " S(z_(4)) are four complex numbers representing the vertices of a rhombus taken in order on the complex plane, which one of the following is held good?

Let f : Z rarr Z be defined as f(n) = 3n for all n in Z . Let g : Z rarr Z be defined as g(n)= n/3 if n is a multiple of 3. g(n)= 0 if n is not a multiple of 3. Show that gof = I_z and fog ne I_Z