# Thread: a + bi form

1. ## a + bi form

Put into a + bi form.

i^102= ?

i^1802= ?

2. Originally Posted by tmac11522
Put into a + bi form.

i^102= ?

i^1802= ?
$i^{102} = i^{100} i^2 = (i^{4})^{25} i^2 = \, ....$

Use the same idea with the second one.

3. $i^1 = i$
$i^2 = -1$
$i^3 = -i$
$i^4 = 1$

the pattern repeats as you continue with higher powers of i

$i^{102} = (i^2)^{51} = (-1)^{51} = -1$

or ...

$i^{102} = i^{100} \cdot i^2 = (i^4)^{25} \cdot (-1) = 1^{25} \cdot (-1) = -1$

so ... $i^{102}$ is a real number (imaginary part is zero).

you try it with $i^{1802}$