Question

How do you simplify `3i^2 - 4i^4 + 5i^8 + 3` and write in a+bi form?

Answer 1

Remember `color(red)(i^2 = -1)` ; `color(blue)(i^4 = 1)`

`3i^2 -4i^4 +5i^8 +3`

Can be rewrite as
`3i^2 -4i^4 _5(i^4)^2 +3`
`=> =3*color(red)(-1)-4*(color(blue)1)+5*color(blue)(1)^2+3`
`=>= -3 -4 +5 +3`
`=> =1`

In `a+-bi` form
`1 +- 0i`