Believe it or not, Imaginary numbers are actually a very REAL thing. No, Some crazy man DIDNT make them up. and yes, you can see them... Imaginary numbers are a result of Radicals. Radicals are Square Roots. Every type of number has a square root... except Negatives (-).

Negative Square Roots are actually what make imaginary numbers. Since there is no squareroot for a regular number, the number is said to be 'imaginary'. We represent imaginary numbers with 'i' (usually in some form of script or cursive handwriting). This 'i' actually equals the square root of -1. So if we have to find a negatives square root, we just divide by -1 to cancel out the negative and then multiply the whole thing by 'i'. Lets look at an example


The Square root of -25 is not -5. The square root of -25 is actually 5i. Lets see how i did it: (i am going to use V¯() as the squareroot symbol)
V¯(-25) --> V¯(25)i --> 5i

What i did was i divided -25 by -1 to give me 25. I put that back inside the square root symbol and then i mulitplied the square root of 25 by 'i'. Thats pretty much it. here are some other problems just for clarification:

V¯(-8) = 2iV¯(2)
V¯(-9) = 3i
V¯(-16) = 4i
V¯(-81) = 9i

 

 

 

Reply

i'm not sure myself, but i think you need to clear up your definition to real numbers. Real numbers are 1,2,3,4,5,6,7,8,9,10 ... , not 5"i". The "i" is still considered as part of the number; therefore, you cannot call 5i a real number.

That's why we called it imaginary, because we have no idea what it is.

lol.. and they taught you this in alegbra 3 & 4 in highschool. But i heard from my brother, when you get into higher math, they will go deeper into what exactly is imaginary number.

Reply

Well I already knew that, but I do have to thank you for telling me a way to make the square root sign without using some weird symbol! Thanks

But wait, what's the third symbol you used? You know, the one with the opposite underscore...

And this is my 1000th post... lol

Reply

Roflmao at least someone learned somthign from my post >.< its alt+0175 to make ¯... and i learned it in Algebra 2 and i know that 'i' is considered apart of the number, because 'i' is not a variable that you have to 'find out' its value, it has a value already that is un-conventional at best :-p ... I actually took algebra 2 last semester XD

Reply

i leanred this in algebra 2... and i got confused with it so lol... im taking the class again to figure it out

Reply

This is pretty simple actually. the square root of any negative number is UNDEFINED. what the imaginary number is doing is simply factoring out the square root of negative 1 so the remainder can be defined.

i, or the imaginary number, is just a concept to be able to manipulate mathematical equations. It is undefined just like infinity. It can't really exist for us.

Reply

I seem to remember my Physics teacher explaining this to me, I didn't really understand it then, maybe it was the fact that it was first thing on a Monday morning (which my don't sleep on Sunday/Monday plan didn't really cater for) but now you've explained it here it seems pretty simple, you don't find the square root of the nagative number you just imagine it to be a real number, this of course makes the answer imaginary (I think thats it anyway), well thanks for the help, have you ever considered teaching? or at least tutoring, you could make some money from stupid people like me.

Reply

And they make some pretty cool looking shapes when they are graphed using Polar Co-ordinates.

Reply

OK there were some wrong things said it is like this.

Imaginary numbers then real numbers then natural numbers. and not real as first and then imaginary.

Also they can be seen either as fractals they are really nice when represented with some fractal function.

But they are usually represented in bipole coordinate system or as it is mostly known to everyone x y axis. In which y axis is actually changed for the imaginary numbers and as imaginary numbers are made of two parts real part and imaginary part you represent imaginary part on y axis and x part will then make real axis and you can see them that is why there is also other representation of the imaginary numbers with the distance from origin and angle with the x axis.

Reply

basically the square root of -1 (negative one) is taken as i and is considered an imaginary and all other square roots of a negative number can be reduced to i. So we might consider i to be the only imaginary number. Its applications lie in Mathematics and Physics, with true practical applicaions at their most advanced levels. Not something we need to worry ourselves over

Reply