>>17005741i ≠ -1
i is a complex number. Complex numbers are pairs of real numbers (x, y) where the y is called "imaginary". If y=0, then complex numbers work exactly like real numbers.
The rules are that there is a complex number i, defined as (x=0, y=1). we define i*i =-1. Then we can write any complex number (x, y) as x + i y, so instead of pairs we can treat them as sums.
This gives rules for addition - (x0, y0) + (x1, y1) = (x0 + i y0) + (x1 + i y1) = (x0 + x1) + i (y0 + y1) = (x0+x1, y0+y1)
And rules for multiplication -
(x0, y0) * (x1, y1) = (x0 + i y0) * (x1 + i y1) = x0x1 + i x1y0 + i x0y1 - y0y1 = (x0x1 - y0y1) + i (x1y0 + x0y1) = (x0x1 - y0y1, x1y0 + x0y1)
all you have to remember is that i^2 = - 1, and how to convert from pairs of real numbers to sums of the real and imaginary parts
