what is the answer to
2^i
2007-06-27 15:10:00 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
is it 2^sqrt(-1)
1/2^sqrt(1)
1/2^1
1/2
?
2007-06-27 15:10:41 · update #1
The answer is actually expressed using Euler's identity, which goes as follows:
e^(ix) = cos(x) + i sin(x)
But 2^i = e^( i ln(2) ), so
e^(i ln(2)) = cos(ln(2)) + i sin(ln(2))
Showing that, for x = ln(2),
2^i = cos(ln(2)) + i sin(ln(2))
2007-06-27 15:16:01 · answer #1 · answered by Puggy 7 · 2⤊ 0⤋
You're going to use Euler's formula and the properties of imaginary numbers to simplify the answer. The answer is likely to not be a real number but a complex number.
2007-06-27 15:16:58 · answer #2 · answered by Anonymous · 2⤊ 0⤋
2^i = 0.769 + 0.639 i
Based on your additional data it's 2^â(-1)
2007-06-27 15:17:30 · answer #3 · answered by davec996 4 · 0⤊ 1⤋
2^i = e^(i ln 2) = cos (ln 2) + i sin (ln 2).
2007-06-27 15:15:45 · answer #4 · answered by Scarlet Manuka 7 · 3⤊ 0⤋
Guessing --- .50?
I'm a Sasquatch, not a math giant!
Nice question though!
The Ol' Sasquatch Ã
2007-06-27 15:14:14 · answer #5 · answered by Ol' Sasquatch 5 · 0⤊ 5⤋