A great man once noted that:
Algebra
Level
2
Also try plugging in Pi.
D
None of the above
E
All of the above.
B
C
F
A
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It is Euler's formula, e i x = cos ( x ) + i sin ( x ) . With some calculus you can derive the formula in a similar way to Euler himself. Simply compare the power series of the three terms.
Euler solved many unsolved problems and contributed plenty of everything to just about everything in mathematics, including geometry, algebra, calculus, number theory, and computer science (yes that's right, he founded graph theory 200 years before electronic computers). Although Euler was the first to apply this formula extensively, others had found similar formulas before. He is in the running for best mathematician of all time, along with Gauss, Erdos, Ramanujan, Leibniz, Euclid, and Descartes.