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

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Answer 1 · 2015-11-27T20:28:05

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
$1 +- 0i$

How do you simplify 3i^2 - 4i^4 + 5i^8 + 33i^2 - 4i^4 + 5i^8 + 3 and write in a+bi form?