solve part B, other parts are included for reference

3. In class we showed how to get real forms from the complex ()=21eimp functions (m=0,1,2,). For problem 1 we gave expressions for the legendre polynomials P20,P21, and P22. Using this information and the normalization constant formula for the legendre polynomial Ntm=[2(l+m)!(2l+1)(lm)!]1/2 and generate normalized angular expressions for the five d-orbitals m=0dz2()= m=1dv()=dy()= m=42dv()=dx2y2(bo)= b) Show that these functions have the expected angular distributions given by their cartesian depictions. c) Show that dz2() is normalized d) Show dy() and du() are orthogonal. e) In problem 2 we showed the sum of the p1,py, and p2 probability densities was independent of angle (spherically symmetric). Is the same true for your results in problem 3