ok i'll take a stab at this,
from my days of Algebra 2,
'^' applies to exponents, ie. x^2 = x squared
i = the square root of -1
i^2 = -1
i^3 = -i because (i^2)(i) = (-1)(i) = -i!
i^4 = 1 because (i^2)( i^2) = (-1)(-1) = 1
i^5 = i because(i)(i^4) = (i)(1) = i!
i^6 = -1 because (i^2)(i^4) = (1)(-1) = -1!
and so on and so on.......
also the square root of a negative number is imaginary, hence the 'i', so the square root of -17 equals just 17i!
these can also be written out so if you have the square root of negative pi, and the square root of negative pi equals the square root of negative 1 times the square root of pi, and the square root of -1 is i, than it can be written out as i root pi! its really hard to explain without pictures.