i = sqt(-1) and i^2 = -1

remember sqt(ab) = sqt(a) * sqt(b)

a + bi is called a complex number

Rationalize complex denominators

Use the conjugate method

2 + 3i / 4 - 2i

(2 + 3i)(4 + 2i)/(4 - 2i)(4 + 2i)

... // here you foil and combine like terms and simplify complex numbers as much as you can

(1 + 8i)/10

Factoring

x = ± sqt(-25)
  = ± sqt(-1) sqt(25)
  = ± 5 * sqt(-1)
  = ± 5i

Powers

i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
i^6 = -1
i^7 = -i
...

So you can simplify large powers of i

i^97 // pull largest possible multiple of 4

i^96 * i

(i^4)^24 * i

1^24 * i

1 * i

i