Answer
$\psi(x)=Ae^{ikx}$
where $A$ and $B$ are constants.
Using Euler's equation, we get
$\psi=A(\cos kx+i\sin kx)$
or, $\psi=A\cos kx+iA\sin kx$
or, $\psi=a+ib$
where, $a=A\cos kx$, and $b=A\sin kx$ are real quantities.
Work Step by Step
$\psi(x)=Ae^{ikx}$
where $A$ and $B$ are constants.
Using Euler's equation, we get
$\psi=A(\cos kx+i\sin kx)$
or, $\psi=A\cos kx+iA\sin kx$
or, $\psi=a+ib$
where, $a=A\cos kx$, and $b=A\sin kx$ are real quantities.
