87-4 The complex forcing function j(at+o) 々eJ(+8 9) N cos(ar +o) jlm sin(ar +9 jIm sin( at+p) Vm cos(at +9) Im cos(at +p jVm sin(at +9)- jIm sin(at+o Vm cos(at+9)+ jvm sin(at+9)-Im cos(at +p)+jIm sin(at +) A real, an imaginary, or a complex forcing function will produce a real, an imaginary, or complex response, respectively. Instead of applying a real forcing function to obtain the desired real response, we apply a complex forcing function whose real part is the given real forcing function; we obtain a complex response whose real part is the desired real response.§7-4 The complex forcing function − + V cos(t +) m jV sin(t +) m jI sin(t +) m I cos(t +) N m V cos(t +) m jV sin(t +) m I cos(t +) m jI sin(t +) m Vm cos(t +) + jV sin(t +) m I m cos(t +) + jI sin(t +) m A real, an imaginary, or a complex forcing function will produce a real, an imaginary, or complex response, respectively. Instead of applying a real forcing function to obtain the desired real response, we apply a complex forcing function whose real part is the given real forcing function; we obtain a complex response whose real part is the desired real response. j( t ) m V e  + j( t ) m I e  +