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A Tschirnhausen transformation can be used to take a general quintic equation to the form x^5-x-a=0, where a may be complex.

Two complex numbers z=x+iy and z^'=x^'+iy^' are added together componentwise, z+z^'=(x+x^')+i(y+y^'). In component form, (x,y)+(x^',y^')=(x+x^',y+y^') (Krantz 1999, p. 1).

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

The Goffinet dragon is the fractal obtained by plotting all points spanned by powers of the complex number p=0.65-0.3i (Trott 2004, p. 9).

The convolution of two complex-valued functions on a group G is defined as (a*b)(g)=sum_(k in G)a(k)b(k^(-1)g) where the support (set which is not zero) of each function is ...

Let |A| be an n×n determinant with complex (or real) elements a_(ij), then |A|!=0 if |a_(ii)|>sum_(j=1; j!=i)^n|a_(ij)|.

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

A theorem proved by É. Cartan in 1913 which classifies the irreducible representations of complex semisimple Lie algebras.

Let K be a finite complex, and let phi:C_p(K)->C_p(K) be a chain map, then sum_(p)(-1)^pTr(phi,C_p(K))=sum_(p)(-1)^pTr(phi_*,H_p(K)/T_p(K)).