Complex Numbers

The standard form of a complex number is the cartesian one; a plane with orthogonal axes for real parts and imaginary parts. A complex number has a pair of co-ordinates defining its position on the plane.

A trigonometric form is a plane with an origin, and one line from the origin to infinity. A complex number is defined by its distance from the origin and the angle between the datum line and the line joining the number to the origin.

It is just like co-ordinate geometry with co-ords r, theta instead of x,y.

It's someone's personal cell phone number in Atlanta Georgia. I deleted everything except the area code and prefix so they won't be getting a million calls.

Real numbers are a proper subset of Complex numbers.

With the exception of zero, which is neither positive nor negative, every real number is either plus or minus. With positive number, the + sign is often implied and therefore is not always written [example: 3 and +3 both mean positive three]

The solutions of a quadratic equation in the form of ax^2+bx+c=0 are the points at which the parabola of ax^2+bx+c=y touches the x axis. An imaginary or complex solution to such a question implies that the parabola touches the x axis at a point not within the real x-y plane; to represent complex or imaginary answers, one must introduce a third dimension, and then the location at which the parabola crosses the y-axis will be apparent.

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In complex mode functions, modules, and procedures cannot operate. For a complex number z = x + yi, first define the absolute value. This would be |z| and is the distance from z to 0 in the complex plane.

Imaginary numbers are numbers whose square is a negative number. They arose as a means of working with square roots of negative numbers; in fact, the first known mention of a square root of a negative number is a very brief one from a work called Stereometrica. It was written in the 1st century CE by a Greek mathematician, Heron of Alexandria. Imaginary (and thus, complex) numbers were not ever accepted widely, though, until the 1700s, because of the work of Euler and Gauss.

It is infinity which can't be exactly determined.

-2

In (a+bi) + (c+di), you add the real parts using the laws for real numbers and do the same for the imanginary parts.

(a+c)+(b+d)i

No. A complex number is a number that has both a real part and an imaginary part. Technically,

a pure imaginary number ... which has no real part ... is not a complex number.

That depends what is the problem given, and what you want to solve. You may want to read an introductory article on complex numbers, to learn how you add them, multiply them, etc.

That depends what is the problem given, and what you want to solve. You may want to read an introductory article on complex numbers, to learn how you add them, multiply them, etc.

That depends what is the problem given, and what you want to solve. You may want to read an introductory article on complex numbers, to learn how you add them, multiply them, etc.

That depends what is the problem given, and what you want to solve. You may want to read an introductory article on complex numbers, to learn how you add them, multiply them, etc.

Relates in many different ways you are constantly working with fractions, there are different formulas for different things like figuring out the rise and run on a set of steps or the rafters to frame a roof.

Sure, if the imaginary part is opposite. For example:(3 + 2i) + (5 - 2i) = 8

figuring you meant are, not or, 5.

distance from point (0,0) to 3+2i is |3+2i| =sqrt(9+4)=sqrt(13)

so the radius of the circle is sqrt(13) and its area is sqrt(13)*sqrt(13)*Pi = 13*Pi = 40.84

electrical engineers and quantum mechanics use them.

Pentabyte

It depends:

7/8/9/10 can be:

7/(8/(9/10)) = 7/(80/9) = 63/80, or

7/((8/9)/10) = 7/(8/90) = 7/(4/45) = 315/4

(7/8)/(9/10) = 70/72 = 35/36

(7/(8/9))/10 = (63/8)/10 = 63/80

((7/8)/9)/10 = (7/72)/10 = 7/720

* * * * *

There is an "and" between 8 and 9 so the question, in fact, refers to 7/8 + 9/10 which is not ambiguous.

7/8 + 9/10 = 35/40 + 36/40 = 71/40 = 1 and 31/40

The square root sign is called a radical

To any set that contains it!

It belongs to {-1},

or {45, sqrt(2), -1, pi, -3/7},

or all whole numbers between -43 and 53,

or square roots of 1,

or negatives of counting numbers,

or integers,

or rational numbers,

or real numbers,

or complex numbers,

etc.

a fraction

No because a billion is 1,000,000,000 which is a thousand million