document.write( "Question 932083: FIND THE VALUES OF i^-i
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Algebra.Com's Answer #565956 by rothauserc(4718) $\"\"$ $\"About$

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i^-i = 1 / i^i
\n" ); document.write( "we start with Euler's formula
\n" ); document.write( "e^(i*pi) + 1 = 0 which implies
\n" ); document.write( "e^(i*t) = cos(t) + (i*sin(t))
\n" ); document.write( "now we can write
\n" ); document.write( "e^(i*(Pi/2)) = cos(Pi/2) + i*sin(Pi/2) = i
\n" ); document.write( "now raise both sides of = to the ith power
\n" ); document.write( "e^(i*i*Pi/2) = i^i
\n" ); document.write( "e^(-Pi/2) = .20788
\n" ); document.write( "therefore
\n" ); document.write( "(1/(i^i)) = (1 / .20788) = 4.810467577
\n" ); document.write( "now note that e^(5i*Pi/2)=i
\n" ); document.write( "i^i has many possible values and i^i is a multi-valued function\r
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