All of us are familiar with real numbers. But numbers having both real and imaginary parts are called complex numbers. A complex number (y) can be denoted as y=a+ib

Where a and b are real numbers and I is an imaginary number (defined as the square root of -1).

In the case of real numbers,
If y=a+b
Then, y2=(a+b)(a-b)
In the case of complex numbers,
If y=a+ib
Then, y2=a+ib (by definition)
In the Schrodinger wave equation, the imaginary part involves time (t instead of b). So the square of wave function cpmtains both forward and backward time-waves travelling both into the past and future.