Changes

The applications include these:

The applications include these:

*Theoretical mathematics:

*Theoretical mathematics:

::algebra (including finding roots of polynomials)

::'''algebra'''— (including finding roots of polynomials)

::linear algebra—vector spaces, inner products, Hermitian and unitary operators, Hilbert spaces, etc.

::'''linear algebra'''—vector spaces, inner products, Hermitian and unitary operators, Hilbert spaces, etc.

::eigenvalue/eigenvector problems<!-- Yes, listing it twice-->

::'''eigenvalue/eigenvector problems'''<!-- Yes, listing it twice-->

::number theory&mdash;This seems improbable, but it is true.  The Riemann zeta function, and the Riemann hypothesis, are very important in number theory.  For a long time, the only proofs of the prime number theorem used complex numbers.  The Wiles/Taylor proof of [[Fermat's Last Theorem]] uses modular forms, which use complex numbers.

::'''number theory'''&mdash;This seems improbable, but it is true.  The Riemann zeta function, and the Riemann hypothesis, are very important in number theory.  For a long time, the only proofs of the prime number theorem used complex numbers.  The Wiles/Taylor proof of [[Fermat's Last Theorem]] uses modular forms, which use complex numbers.

::trigonometry&mdash;finding arcsine and arccosine functions of numbers with [[absolute values]] more than 1 or arcsecant and arccosecant functions with absolute values between 0 and 1.

::'''trigonometry'''&mdash;finding arcsine and arccosine functions of numbers with [[absolute values]] more than 1 or arcsecant and arccosecant functions with absolute values between 0 and 1.

*Applied mathematics

*Applied mathematics

::eigenvalue/eigenvector problems

::'''eigenvalue/eigenvector problems'''

::Fourier and Laplace transforms

::Fourier and Laplace transforms

::linear differential equations

::linear differential equations