1. I have recently committed myself to comprehending complex numbers. In trying to find a place to start that succinctly defines the nature of numbers, I feel the best place to start is with understanding the construction to i, or, the square root of -1.

2.

4. is the start. Everything else follows from that.

5. is just another way of writing

6. Originally Posted by Arcane_Mathematician
is just another way of writing
this much I comfortably comprehend. It is the solution that i represents that I am trying to grasp.

7. Originally Posted by Re-strained
Originally Posted by Arcane_Mathematician
is just another way of writing
this much I comfortably comprehend. It is the solution that i represents that I am trying to grasp.
To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......

8. Originally Posted by Re-strained
It is the solution that i represents that I am trying to grasp.
Don't think that way. is your starting point. All else follows from that and the rules of arithmetic.

9. Originally Posted by KJW
Originally Posted by Re-strained
It is the solution that i represents that I am trying to grasp.
Don't think that way. is your starting point. All else follows from that and the rules of arithmetic.
OK. Will go from there. Thanks for setting me up for a challenge. I hope my answer matches your own.

10. Originally Posted by Re-strained
Originally Posted by Re-strained
Originally Posted by Arcane_Mathematician
is just another way of writing
this much I comfortably comprehend. It is the solution that i represents that I am trying to grasp.
To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
ie, providing i with a value identifies the equilibrium associated to 0......

11. Originally Posted by Re-strained
ie, providing i with a value identifies the equilibrium associated to 0......
I don't know what that means. As others suggest, I would concentrate on the algebraic/arithmetic properties of i and the complex numbers.

If you want to give it meaning, then look at the complex plane and consider multiplication by i as rotation by 90° (and multiplication by -1 as rotation by 180°).

12. Originally Posted by Strange
Originally Posted by Re-strained
ie, providing i with a value identifies the equilibrium associated to 0......
I don't know what that means. As others suggest, I would concentrate on the algebraic/arithmetic properties of i and the complex numbers.

If you want to give it meaning, then look at the complex plane and consider multiplication by i as rotation by 90° (and multiplication by -1 as rotation by 180°).
Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.

13. [QUOTE=Strange;506365]
Originally Posted by Re-strained

If you want to give it meaning, then look at the complex plane and consider multiplication by i as rotation by 90° (and multiplication by -1 as rotation by 180°).
That is useful information certainly. Thank you.

14. Originally Posted by Re-strained
Originally Posted by Re-strained
To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
ie, providing i with a value identifies the equilibrium associated to 0......
Originally Posted by Re-strained
Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
Welcome back, 3SwordBunny.

15. Originally Posted by Re-strained
Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
Oh boy...

16. Originally Posted by Strange
Originally Posted by Re-strained
Originally Posted by Re-strained
To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
ie, providing i with a value identifies the equilibrium associated to 0......
Originally Posted by Re-strained
Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
Welcome back, 3SwordBunny.
Thank you for helping unmuddle my question. First time in 20 years my head has not spun when I think about it. Helps...

17. Originally Posted by Re-strained
Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
Why are you typing like that? It makes you look silly, not smart.

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