It's e^(iπ) + 1 = 0 Considered one of the most amazing equations in mathematics, because it uses an imaginary i, two irrational numbers, e and π, along with 1 and 0, and also all the properties, addition, multiplication, exponential.
2006-12-23 08:31:24 · 4 answers · asked by scrabbler 1 in Science & Mathematics ➔ Mathematics
Yeah pretty cool huh? Euler (pronounced Oiler) was a Swiss who was so proficient he worked until his 70s or 80s, and some of his stuff has yet to be translated! He was the exception to the rule that most mathematicians seem to decrease in creativity after age 40.
Give me the best answer please...thanks!
2006-12-23 09:34:36 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The Euler's equation is
e^(ix) = cos x + i sin x
You just plugged x = pi
which equals cos pi + i sin pi + 1 = -1 + i (0) +1 = 0
2006-12-23 08:42:48 · answer #2 · answered by Sheen 4 · 0⤊ 0⤋
If you take the power series for e^z and plug in z=i*pi and collect terms you'll get and equation relating the power series for cos and sine:
e^z = cos(z)+i*sin(z)
2006-12-23 08:49:40 · answer #3 · answered by modulo_function 7 · 0⤊ 0⤋
whoopie!
2006-12-23 09:09:56 · answer #4 · answered by csulbalgebra 2 · 1⤊ 2⤋