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A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

A complex fraction is a fraction in which numerator, denominator, or both are themselves fractions, for example (2/3)/(4/5).

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

A connection defined on a smooth algebraic variety defined over the complex numbers.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

A Hermitian inner product space is a complex vector space with a Hermitian inner product.

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... the module Z_i of i-cycles is the kernel of d_i, which is a submodule of C_i.

The axis in the complex plane corresponding to zero real part, R[z]=0.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

An algorithm which isolates roots in the complex plane by generalizing one-dimensional bracketing.