What's an "imaginary" number?

Question

Thanks for your help!

Answer 1

an imaginary number is a real number times the square root of negative one. There is a graphical interpretation of this. If you say the y-axis is the imaginary value, and the x-axis is the reals then your coordinates are (real number, imaginary number) -- like (2,3i). It is a bit confusing because the first place you learn them is in the quadratic equation. They are the "imaginary" answers to when the graph crosses the x-axis. Don't worry if that doesn't make sense to you because mathematicians of long ago didn't buy that answer either. Problem is they show up in the cubic polynomial too -- x^3+x^2+x+1=0. Here is a graph of this function -- http://upload.wikimedia.org/wikipedia/commons/f/fa/Polynomialdeg3.png

From this we can see that the graph MUST cross the x-axis, so the fact that we get imaginary numbers in the equation for the cubic forces us to accept them.

If you can accept that sqrt(2) i-- irrational (cannot be made into a fraction and the digits go on forever and never repeat) -- is a number and that pi -- transendental (cannot be made into any finite combination of numbers using +,-,division, mult., square or square root) then it should be easy to accept the square root of -1 as a number. Pi is the easiest way to write that number and the square root of -1 is the easiest way to write the complex number -- it is irreducible because -1 doesn't have a square root.

Imaginary numbers are needed to make some problems in advanced math easier, and sometimes they are needed to solve an equation.

Answer 2

The square root of a negative number.

An imaginary number is written with an i

(A bit of revision ...... 3 x 3 = 9 and .......-3 x -3 = 9, so until you learn about imaginary numbers, you just say "square root of a minus number?...I can't do it)

Now you learn the next step and you can find the square root of negative numbers.

The square root of -1 is called i
i x i = -1

2i x 2 i = -1 x 2 x 2 = -4,

So the square root -4 = 2i

Similarly, the square root of -25 = 5i

So now you know how to work out the square roots of ....

-64, -36, -144 and -169

Good luck

Answer 3

Sort of an unfortunate fluke of history.

Consider
x^2+1 = 0 , a perfectly nice algebraic equation. It caused fits because it has a solution of x = sqrt (-1). So, let's call it i and use it like a regular number, noting that i^2=-1.

This worked great because now ALL algebraic equations have a solution. Complex number have a real and an imaginary part and are essential. They also are quite real in their usefulness in solving problems in electromagnetics, heat transfer, fluid dynamics.

So, they are only imaginary in the sense that they don't represent something that can be measured. Irrational numbers caused fits with the Greeks because they had a very geometric concept of a number. Hence they had a hard time 'wrapping their head' around sqrt(2).

Answer 4

It came about when mathemeticians pondered about what to do or how to make use of the square root of negative numbers. They finally decided to call the square root of -1 the letter i.

Thus i = sqrt (-1)
i^2 = -1
i^3= -i
i^4=1
i, of course , stands for imaginary because it does not exist.

Numbers like 6i are called pure imaginary.
Numbers like 3+6i are called complex numbers because they have a real part (3) and an imaginary part (6).

Mathemeticians have made i an important part of mathematics which you will learn about in mor advanced mathematics.

I hope I didn't tell you more than you wanted to know.

Cheers.

Answer 5

An imaginary number is one that contains the term "square root of -1" Because there is no way to take the square root of a negative.

Answer 6

a+ib is a complex number. It has two parts.
a is the real part. ib is the imaginary part. i stands for sqrt-1. Many problems which can not be handled in the real domain can easily be solved in the imaginary domain. Hence the need for imaginary number or complex numbers.

Answer 7

Let's say you have the square root of -2. You can't have that, so you break that down into the square root of 2 and the square root of -1. The square root of -1 is written as i. i^2 equals -1. when you see a number like 2i, that means it's 2-1. 2i^2 is 2(-1) or -2.

Answer 8

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Answer 9

a number relation to the square root of -1.

Answer 10

Eleventy.