document.write( "Question 1075983: Can somebody fill me in a bit on Euler’s formula?\r
\n" ); document.write( "\n" ); document.write( "e^(a + bi) = e^a*(cos b + i sin b) -- Euler's Formula.\r
\n" ); document.write( "\n" ); document.write( "His equation gives rise to e^(πi) + 1 = 0. \r
\n" ); document.write( "\n" ); document.write( "'0, 1,π , e, and i' Are all in one equation. \r
\n" ); document.write( "\n" ); document.write( "Could you explain how Euler’s formula could be applied to derive this equation? Thank you very much. \n" ); document.write( "

Algebra.Com's Answer #690680 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"e%5E%28a%2Bbi%29=e%5Ea%2Ae%5E%28bi%29\"$
\n" ); document.write( "OK so when $\"a=0\"$ and $\"b=pi\"$ ,
\n" ); document.write( " $\"e%5E%280%2Bpi%2Ai%29=e%5E0%2A%28cos%28pi%29%2Bi%2Asin%28pi%29%29\"$
\n" ); document.write( " $\"e%5E%28pi%2Ai%29=1%28-1%2Bi%2A0%29\"$
\n" ); document.write( " $\"e%5E%28pi%2Ai%29=-1\"$
\n" ); document.write( " $\"e%5E%28pi%2Ai%29%2B1=0\"$
\n" ); document.write( " \n" ); document.write( "

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