Search Results for ""

A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

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 ...

Pre-Calculus

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

A quadratic field Q(sqrt(D)) with D>0.

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

A complex number may be taken to the power of another complex number. In particular, complex exponentiation satisfies (a+bi)^(c+di)=(a^2+b^2)^((c+id)/2)e^(i(c+id)arg(a+ib)), ...