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The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy ...

The modulus of a complex number z, also called the complex norm, is denoted |z| and defined by |x+iy|=sqrt(x^2+y^2). (1) If z is expressed as a complex exponential (i.e., a ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself, R[z]=1/2(z+z^_), where z^_ is the complex conjugate of ...

The set A^2 of all ordered pairs of complex numbers.

In the archaic terminology of Whittaker and Watson (1990), the complex number z representing x+iy.

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^').

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

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

A pair of values x and y one or both of which is complex.