AOA... I wan to plot the following piecewise function

f := x^2+1         if x belongs to (0,1)

f := x-x^2          if x belongs to (1,2)

f := x+1-x^2       if x belongs to (2,3)

AOA... There are three question

1. I want to convert exp(Iota*theta) into ternometric function i.e., 

exp(Iota*theta) = cos(theta)+Iota*sin(theta)

Is there any comand pl help...

2. Also i want to rationalize the complex number...

3. I want to seprate real and imaginary parts of a comaplex numbers

I want to introduce a matrix of order M by M as for any m, M, pl help as show in file

Help.mw

AOA... I want to solve the following system in maple pl help

sys_ode := diff(y(eta), eta, eta, eta)+3*y(eta)*(diff(y(eta), eta, eta))-2*(diff(y(eta), eta))^2+x(eta) = 0, diff(x(eta), eta, eta)+3*Pr*y(eta)*(diff(x(eta), eta)) = 0

ics := y(0) = 0, (D(y))(0) = 0, (D(y))(infinity) = 0, x(0) = 1, x(infinity) = 0

Help.mw

AOA... Pl correct it

Help.mw