Thread: Resources for complex numbers

Hello, Cyf here.

I'm attempting to learn about complex numbers and I was wondering if anyone had any resources? I've gotten as far a complx conjugates because I have no idea what they are and I've also been given this diagram which I don't understand. Could anyone explain it to me and explain what is arg(z)?

I don't differentiate between books or sites, as long as either are clear, simple and for the amateur (self-studying, never done this before)

Any help greatly appreciated.

~Cyf

Edit: I forgot to ask, what does a triple dash mean? Like an equals sign but with one more hyphon in it.

Edit: Sorry for forgetting the diagram. Here it is:

a + ib and a - ib are complex conjugates (their product is a^2 + b^2) where a and b are real numbers.

A triple dash means identical.

I understand how it means congruent/identical in geometrical shapes but not in algebra

For complex conjugates I was referring to circumstances such as z*

Complex Conjugate Pairs

what is meant by a commer (apologies for the mutation of a language if this is spelt incorrectly) between two values?

Originally Posted by Mukilab

what is meant by a commer (apologies for the mutation of a language if this is spelt incorrectly) between two values?

I believe you mean either a comma or an apostrophe (need more context or an example).

Originally Posted by wonderboy1953

I believe you mean either a comma or an apostrophe (need more context or an example).

comma

u,v

Originally Posted by Mukilab

comma

u,v

For example the comma in 238,231 means the number is over 238 thousand (the comma is being used to make it easier to understand the number).

Do you have something else in mind when you say values?

" Let l = (u, v) be a complex number,"

Originally Posted by Mukilab

" Let l = (u, v) be a complex number,"

u + iv = 1 is what the comma means in this instance.

Why is it written in the form (u,v)?

Originally Posted by Mukilab

Why is it written in the form (u,v)?

It's an abbreviation since the i is well understood; also it helps out in complex coordinate geometry (with Argand diagrams).

will something such as (a,b) always be a+ib or could it be ia+b or even a-ib?

a - ib is the complex conjugate to a + ib so the answer is no there, the other expression ia + b is also regarded as being different since a precedes b (another way of saying this is that order matters).