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Consider the expression (cos(theta) + i*sin(theta))⁵ . (Where theta a real parameter).By De Moirve's theorem, we know this expression is equivalent to cos(5theta) + i sin(5theta).We can also ap...

The system is described by a homogeneous, second order differential equation d²x/dt² +(dx/dt * c/m) + kx/m =0. First, substitute the known constants (m,k,c) to get d²x/dt<...

The eigenvalues are given by the characteristic equation (1-x)((1-x)^2-4)=0, which gives the values x=1, x=-1 and x=3 . These eigenvalues correspond to the eigenvectors (0, 1, 0), (1, -1, -1) and (1, -...