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As a complex number, i can be represented in rectangular form as 0 + 1i, with a zero real component and a unit imaginary component. In polar form, i can be represented as 1 × e πi /2 (or just e πi /2), with an absolute value (or magnitude) of 1 and an argument (or angle) of radians.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, ... Negative one: −1 −1 300 to 200 BCE Cube root of 2 ...
The principal cube root is its principal value, that is a unique cube root that has been chosen once for all. The principal cube root is the cube root with the largest real part. In the case of negative real numbers, the largest real part is shared by the two nonreal cube roots, and the principal cube root is the one with positive imaginary part.
by the functional equation and Euler's identity. For example, e iπ = e 3iπ = −1, so both iπ and 3iπ are possible values for the complex logarithm of −1. In general, given any non-zero complex number w, any number z solving the equation = is called a complex logarithm of w, denoted .
y = x 3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square:
An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
The degree of the zero polynomial is either left undefined, or is defined to be negative (usually −1 or ). [7] Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial. It has no nonzero terms, and so, strictly speaking, it has no degree either.
A value of 1 produces a cube, 0 produces a cuboctahedron, and negative values produces self-intersecting octagrammic faces. If the self-intersected portions of the octagrams are removed, leaving squares, and truncating the triangles into hexagons, truncated octahedra are produced, and the sequence ends with the central squares being reduced to ...