# complex number

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Related to Imaginary plane: imaginary part, Imaginary axis, Argand plane

## complex number:

see number**number,**

entity describing the magnitude or position of a mathematical object or extensions of these concepts.

**The Natural Numbers**

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their

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## complex number

[′käm‚pleks ′nəm·bər] (mathematics)

Any number of the form

*a*+*bi*, where*a*and*b*are real numbers, and*i*^{2}= -1.## complex number

any number of the form

*a*+ i*b*, where*a*and*b*are real numbers and i = ÝA--1## complex number

(mathematics)A number of the form x+iy where i is the square
root of -1, and x and y are real numbers, known as the
"real" and "imaginary" part. Complex numbers can be plotted
as points on a two-dimensional plane, known as an Argand diagram, where x and y are the Cartesian coordinates.

An alternative, polar notation, expresses a complex number as (r e^it) where e is the base of natural logarithms, and r and t are real numbers, known as the magnitude and phase. The two forms are related:

r e^it = r cos(t) + i r sin(t) = x + i y where x = r cos(t) y = r sin(t)

All solutions of any polynomial equation can be expressed as complex numbers. This is the so-called Fundamental Theorem of Algebra, first proved by Cauchy.

Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity.

An alternative, polar notation, expresses a complex number as (r e^it) where e is the base of natural logarithms, and r and t are real numbers, known as the magnitude and phase. The two forms are related:

r e^it = r cos(t) + i r sin(t) = x + i y where x = r cos(t) y = r sin(t)

All solutions of any polynomial equation can be expressed as complex numbers. This is the so-called Fundamental Theorem of Algebra, first proved by Cauchy.

Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity.

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