Complex Numbers, Part 3 - The Complex Plane

[HolmesProductions1]

what software do you use? i need to plot numbers on the Complex Plane, but i don't know how to do it on the computer. i tried microsoft excel and it didn't work. do you know of any free/cheap software with the Complex plane? i need this for a math project for school. thanks so much.

by the way, i really liked your explanation, it was really easy to understand.

[yamenhawit]

good handwriting.

[yamenhawit]

Who the heck is this guy?

[MilitaryMan006]

What tool is being used in the video?

[SanQae]

You're way better than mr. Khan, Derek. Thank you a lot

[Deaume]

Is there a higher degree of numbers ? Is there equations that Complex Numbers can't solve, in the same way that Real Numbers can't solve some equations ?

[07alanhahn]

Why don't they teach component addition at the same time as this in school? I believe it would clear up alot about this, and about graphing in general. (When I mean component addition, I mean something like adding vectors, such as (3,2)+(5,1) = (8,3)) What do you think?

[alexhamster1134]

@GrimmIII while holding the textbook upside down :p

[schnizelcreep]

dont you gotta draw a ray towards that point?

[alexhamster1134]

is it me or does he sound a bit like george dubaya bush?

[derekowens]

@alexhamster1134 Haha! No, it's not just you, apparently. I've never had a student in class say that, but about 20 or so people on YouTube have made a similar comment. Not sure why, but it's kind of funny!

[alexhamster1134]

@derekowens a young george dubuya.... it must be the way you draw out the last syllable through your nose...

[sixstringbrad1]

@alexhamster1134 ive never heard him sound so smart!

[piratecheese13]

@alexhamster1134 no way dubblejah could do this

[alexhamster1134]

@piratecheese13 doe his brother count? (ie the guy talking in this video)

[BiggerThinking1]

@alexhamster1134 "Fool me once, shame on (uh) ...shame on... (uh) ...me? - point is a fool cant get fooled again"

WAAAAAAAAAHAHAHAHAHAHA

[alexhamster1134]

@BiggerThinking1 who caught osama? who caught osama? obumma.

[RUL1S88]

@alexhamster1134

it is you.

[alexhamster1134]

@RUL1S88 i must have good hearing

[gillomatallo]

can we think of something like metaphysical calculation using complex number

[gillomatallo]

someone please explain me what is the difference between real line and imaginary line. it appears to me that the two are equivalent in all aspects except in their orientation.

[arjunmax7]

@gillomatallo

The real line represents real numbers while the complex line does it for imaginary nos.

so if we locate a no. on the plane with real coordinate 2 and imaginary coordinate 3 then the number is 2+3i

its just a way of representing complex numbers with ease

[derekowens]

I think the term "Argand Diagram" is more common in Europe, while the term "Complex Plane" is more common in the US. They are the same thing, though.

It ultimately doesn't matter whether the i comes before the number or after. Two times i is the same as i times two, and it's just multiplication. "a + bi" is sometimes referred to as the "standard form", but "a + ib" is mathematically equivalent.

Glad you like the videos!

Derek Owens

[derekowens]

Isn't the proper name for this an Argand Diagram?

Or should I be using the name 'Complex Plane'?

And should the 'i' only be after the number in Algebra? I've been told to put it before the number, not sure if it matters.

Your lessons are very easy to follow though, better than my lecturer lol

[PandaBasher]

You're videos are very helpful and very approachable and understandable. Thanks. :)

[GR1o6180339887498948]

From the fundamental theorem of algebra we know that we don't need any other numbers besides complex numbers, but do you know if there are any others after the complex numbers? I think that there can be infinite sets of numbers out there but I don't know if any one has developed new numbers with their required properties such as the field properties of complex numbers that include the additive abilian group, the ring, and so on.

[derekowens]

I don't know about the specifics you mentioned (abilian group, the ring, etc) but I do know that Abraham Robinson did some work in the 1960's with hyperreal numbers. These are infinitely small numbers (think dx and dy) and their reciprocals, which are infinitely large. His ideas form a coherent and rigorous foundation for an intuitive approach to Calculus, like that of Leibniz, without all the Cauchy and Weierstrauss work on limits. IMO, this is pretty important stuff.

[GR1o6180339887498948]

@derekowens

This is great information, thank you.

As for the terms "abelian group", and "ring", these are used in abstract algebra.

If you google "abstract algebra" click on the first Wikipedia article and click on the hyperlink "ring". There you'll find the article that explains it all.

[rafal48]

complex numbers are great, we had an introduction back in high school, but I never really understood why would we need such a imaginary number. Where could we possibly use it?

[derekowens]

There are some problems that are commonly solved using complex numbers. The most common example is probably from electrical engineering. Certain calculations are worked out using complex numbers, and then at the end the real part is taken as the meaningful answer.

[njfife]

Basically it is helpful in Electrical engineering. Specifically in equations involving AC current. Without them math in circuits using AC current would be impossible.

[knownbeforetime]

Alright, I never learned about this in high school... Although, when I first heard of imaginary numbers, I somehow intuitively knew it had something to do with a 2-dimensional plane...

[derekowens]

That's some pretty powerful intuition! Good thinking, there.

[MrRichyou]

Why aren't there more teachers like you ?

[pure0pwnage]

~3xc3ll3nt~ vid3o

v3ry much h3lpful ind33d

[nilsi1987]

love this, thanks.

[Michel290389]

Thanks! Great tutorial series!

[J21C412D0]

i thought for solving on the D point it would be : -4+i -> -4+0i which is (-4,0) ??? so it would only b -4 on the real plane?

[derekowens]

Good question. The number -4 + i is equivalent to -4 + 1i, which is not the same thing as -4 + 0i.

You are correct that -4 + 0i would be on the real number line, but -4 + i1 is complex.

In other words, when we see i by itself, the coefficient is assumed to be 1. Something like x^2 + 2x + 5. The coefficient on the x^2 term is 1 rather than zero.

[martymilan]

you are really brilliant.Great explanations.God bless you