On the Subject of the Cooler Complex-Resistance Strategy

To fit the theme, we made this more complex than it should’ve been.

Continually multiply the displayed number by i until the real and imaginary parts of the obtained number are both non-negative (Note that i²=-1). Start at the row labeled with the number of multiplications required.

Convert each component to a binary number, padding the shorter binary number with leading zeroes until they have equal length, and cross-reference each column from the least significant bit to the most significant bit, moving down after each pair of bits referenced, wrapping around to row 0 as necessary.

Re	0	1	0	1
Im	0	0	1	1
0	00	+0	-+	0+
1	00	+-	+0	0+(-)
2	00	-0	+-	0-
3	00	-+	-0	0-(+)

If, during cross-referencing, a pair of parentheses is obtained, append the cell contents without parentheses to the answer, then cross-reference the symbols inside parentheses with the cell content obtained from the next bit pair (or 00 if there is no bit pair left) in the following table, and append the resulting cell content to the answer instead.

carry	(-)	(+)	(-+)	(+-)
00	-0	+0	-+	+-
-0	00(-+)		0-(+)
+0		00(+-)		0+(-)
0-	--
0+		++
-+		0+	00(+)
+-	0-			00(-)
0-(+)			-0(+)
0+(-)				+0(-)