# My Favorite One-Liners: Part 86

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

To get students comfortable with $i = \sqrt{-1}$, I’ll often work through a quick exercise on the powers of $i$:

$i^1 = i$

$i^2 = -1$

$i^3 = -i$

$i^4 = 1$

$i^5 = i$

Students quickly see that the powers of $i$ are a cycle of length 4, so that $i^5 = i \cdot i \cdot i \cdot i \cdot i$ is the same thing as just $i$. So I tell my students:

There’s a technical term for this phenomenon: aye-yai-yai-yai-yai.

See also http://mentalfloss.com/article/52790/where-did-phrase-aye-yai-yai-come for more on the etymology of this phrase.

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