Simplifying
(j + -1k)(j + -1k)

Multiply (j + -1k) * (j + -1k)
(j(j + -1k) + -1k * (j + -1k))
((j * j + -1k * j) + -1k * (j + -1k))

Reorder the terms:
((-1jk + j2) + -1k * (j + -1k))
((-1jk + j2) + -1k * (j + -1k))
(-1jk + j2 + (j * -1k + -1k * -1k))
(-1jk + j2 + (-1jk + 1k2))

Reorder the terms:
(-1jk + -1jk + j2 + 1k2)

Combine like terms: -1jk + -1jk = -2jk
(-2jk + j2 + 1k2)