I want to understand math . I have posted a picture of math in book " A textbook of Physics" above .
I want to know especially
x= A1(coswt + i sinwt ) + A2 ( coswt - i sinwt )
= (A1 + A2 ) coswt + ( A1i - A2i ) sinwt
= A3 coswt + A4 sinwt
here we supposed an imaginary number to be A4
A3 = a sin B
A4 = a cosB
It shows that either cos B or A4 is imaginary .... Is'nt it?
then we do x = asin B cos wt + a sin wt cos B
when cos B = imaginary then B is imaginary so is sin B
then finally finding solution we do
x = a sin ( wt + B )
which I thought should have been imaginary soulution . but it works well .
So I think I was missing something here . I ho[e you get me now.
In the picture above we add 2 solutions of x give a general solution of x how is that possible.