Page 212 - 'Blast_Into_Math

Blast into Math! Analatic nummer theora: ants, ghosts and giants

Because i = −1, what is i ? Well, i = i ∗ i , and you know i = −1. Then, what is i ?
2
2
3
3
4
2
In general, what is the pattern when you raise i to powers? Use this pattern to relate the
definition of
∞ (iπ) n
iπ

e =
n!
n=0
to the functions sin(x) and cos(x) for x = π. . In trigonometry and geometry, you have
already learned what sin(π) and cos(π) are. Putting all these pieces together you can solve
the problem and prove one of the most famous mathematical formulas of all time,

iπ
e + 1=0.

• Hint for #9: For the first question, think about similar triangles. For the second question,
remember this is a * problem…

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