&=A\;e^{\,i\,\varphi}\cdot e^{\,i\,(\omega t - kx)}\\
&\\
&\color{brown}{\boldsymbol{\mathbf{\large{=\underline{A}\cdot e^{\,i\,(\omega t - kx)}}}}}
\end{align}`$
1D : **$`\quad\large{\boldsymbol{\mathbf{\underline{U}(x,t)}}`$** $`\;= A\cdot exp\,[\,i\,(\underbrace{\omega t - k x + \varphi}_{\color{blue}{exp(a+b) = exp(a)\times exp(b)}})\,]`$
<br>
$`\quad\quad\quad\quad\quad\quad =\underbrace{A\;e^{\,i\,\varphi}}_{\color{blue}{\underline{A}=A\; exp (\,i\varphi))}}\cdot exp\,[\,i\,(\omega t - kx)\,]`$
<br>
**$`\quad\quad\quad\quad\quad\quad\boldsymbol{\mathbf{\large{=\underline{A}\cdot e^{\,i\,(\omega t - kx)}}}}`$**
<br>
3D : **$`\quad\large{\boldsymbol{\mathbf{\underline{U}(\vec{r},t)=\underline{A}\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r})}}}}`$**