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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]
A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the so-called imaginary unit, whose meaning will be explained further below. For example, 2 + 3 i is a complex number.
All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.
The imaginary unit i in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis.. The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0.
Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
In complex analysis, the complex numbers are customarily represented by the symbol z, which can be separated into its real (x) and imaginary (y) parts: z = x + i y {\displaystyle z=x+iy} for example: z = 4 + 5 i , where x and y are real numbers, and i is the imaginary unit .
The symbol i in mathematical equations may refer to; Imaginary unit (i), for which i 2 = -1 Imaginary number;
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...