Simplify i^38

i
-1
-i
1

Question

Simplify i^38

	i
	-1
	-i
	1

anonymous · Answer

divide $38$ by 4 and take the integer remainder
i.e. the remainder is 2
that makes $i^{38}=i^2=-1$

anonymous · Answer

so B? thank youuu

anonymous · Answer

ok i don't get why you divided 38 by 4.. @satellite73

jim_thompson5910 · Answer

You could do it the long way

$$\Large i^{38} = i^{36+2}$$

$$\Large i^{38} = i^{36}*i^{2}$$

$$\Large i^{38} = i^{4*9}*i^{2}$$

$$\Large i^{38} = (i^{4})^{9}*i^{2}$$

$$\Large i^{38} = (1)^{9}*(-1)$$

$$\Large i^{38} = 1*(-1)$$

$$\Large i^{38} = -1$$

But satellite73's shortcut is much simpler

anonymous · Answer

still dont get it :(

anonymous · Answer

im gonna post another question similar.

jim_thompson5910 · Answer

$$\Large i^0 = 1$$

$$\Large i^1 = i$$

$$\Large i^2 = -1$$

$$\Large i^3 = -i$$

$$\Large i^4 = 1$$

Notice how i^0 = i^4. So the pattern repeats every 4 times

jim_thompson5910 · Answer

So that's why he divided by 4. The remainder tells you where in the pattern you are (no matter how huge the exponent gets)