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**

Again

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.