mathematical method of physics

3sin(4x) + 4cos(10x) = 3[sin(4x) + 4cos(4x)cos(6x)] + 4cos(10x) = 3[sin(4x) + 4cos(4x)(cos(6x) + isin(6x))] + 4cos(10x) = 3[sin(4x) + 4cos(4x)e(i6x)] + 4cos(10x) = 3[sin(4x)e(i0x) + 4cos(4x)e(i6x)] + 4cos(10x)e(i0x) = sin(4x)e(i0x) + 4cos(4x)e(i6x) + 4cos(10x)e(i0x) Therefore, the expansion of 3sin(4x)+4cos(10x) in to a functional series of e(exp)ix is given by: sin(4x)e(i0x) + 4cos(4x)e(i6x) + 4cos(10x)e(i0x).