Some basic concepts in quantum field theory part 1

I have some problems about basic concepts of quantum field theory.

First let’s look at Klein-Gordon field.

Klein-Gordon equation has two branches of solutions, one of which is positive frequency and the other is
negative frequency. The solution can be written as
$$psi(x)=int frac{d^{3}p}{(2pi)^{3}}frac{1}{sqrt{2E_{p}}}(a_{p}e^{-ipx+iomega t}+b_{p}e^{-ipx-iomega t}).$$

Then we need to quantize above solution. In the exercise part of both books, Peskin and Srednicki, the complex scalar field operator is written as

$$hat{psi}(x)=int frac{d^{3}p}{(2pi)^{3}}frac{1}{sqrt{2E_{p}}}(hat{a}_{p}e^{-ipx}+hat{b}_{p}^{+}e^{ipx})tag{1}$$

The question is:

Why equ(1) is not written as
$$hat{psi}(x)=int frac{d^{3}p}{(2pi)^{3}}frac{1}{sqrt{2E_{p}}}(hat{a}_{p}e^{-ipx}+hat{b}_{p}e^{ipx})~?$$ Is this because when quantizing negative frequency, annihilation operator must be replaced by creation operator and $-p$ by $p$ in exponent?