How to draw the graph of the complex number solution of X^2+1=0 in the coordinate system? Can anyone help me? Thank you.

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How to draw the graph of the complex number solution of X^2+1=0 in the coordinate system? Can anyone help me? Thank you. [Copy link]

 

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How to draw the graph of the complex number solution of X^2+1=0 in the coordinate system? Can anyone help me? Thank you.

I don't understand what the picture below means. Can you help explain it to me? Thank you.

maychang

"How do you draw the graph of the complex number solution of X^2+1=0 in the coordinate system?"

The solution of X^2+1=0 is two complex numbers, and the image of a number in the complex plane coordinate system is a point, so the image of the complex number solution of X^2+1=0 in the coordinate system is two points. These two points are on the vertical axis (imaginary axis), with the horizontal coordinate being zero and the vertical coordinates being +i and -i respectively.

maychang

There is no need to specifically mention "the complex number solution of X^2+1=0" because X^2+1=0 has no real number solution at all.

chunyang

The solution of X^2+1=0 is i and -i, which are two points in the coordinate system. As for how to draw it, it depends on the definition of the coordinate system. You should look at the textbook for this question. How can you forget such basic things as high school algebra?

深圳小花

chunyang posted on 2021-12-17 12:52 The solution of X^2+1=0 is i and -i, which are two points in the coordinate system. As for how to draw it, it depends on the definition of the coordinate system. You should look at the textbook for this question. High school algebra...

Thank you. I feel like I didn't learn it thoroughly in school. I'm learning Maxwell's equations recently. I didn't learn it in college. It's quite difficult and involves a lot of basic concepts, so I have to study them in depth.

chunyang

Shenzhen Xiaohua published on 2021-12-17 13:19 Thank you. I feel like I didn't learn it thoroughly when I was in school. I'm learning Maxwell's equations recently. I didn't learn it in college. It's quite difficult and involves a lot of...

A complete waste of time...

If you really want to learn advanced things, first relearn the simplest things that you think you know.

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chunyang posted on 2021-12-17 13:33 It's a complete waste of time... If you really want to learn advanced things, first relearn the simplest things that you think you know.

Thank you. I guess I have to start over from kindergarten.

maychang

Shenzhen Xiaohua published on 2021-12-17 13:19 Thank you. I feel like I didn't learn it thoroughly when I was in school. I'm learning Maxwell's equations recently. I didn't learn it in college. It's quite difficult and involves a lot of...

"I've been studying Maxwell's equations recently."

I remember you said you didn't study general physics in college, and from your previous posts I can see that you really didn't study it.

Since you have not learned general physics, you will not be able to understand Maxwell's equations now. Maxwell's equations are partial differential equations, and most of the quantities in the equations are vectors.

maychang

Shenzhen Xiaohua published on 2021-12-17 13:19 Thank you. I feel like I didn't learn it thoroughly when I was in school. I'm learning Maxwell's equations recently. I didn't learn it in college. It's quite difficult and involves a lot of...

Moreover, according to your previous posts, you don't even have a good grasp of the calculus of one-variable functions, otherwise you wouldn't ask questions about the same-order infinitesimals and higher-order infinitesimals. In fact, higher-order infinitesimal problems are very easy to solve, just apply L'Hopital's rule.

If you haven't mastered the calculus of single-variable functions well, it will be impossible to understand the system of partial differential equations well.

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maychang posted on 2021-12-17 14:30 Moreover, according to your previous posts, you don’t even have a good grasp of the calculus of one-variable functions, otherwise you wouldn’t ask questions about the same-order infinitesimals and higher-order infinitesimals...

grateful.

maychang

Let’s go back to the curve shown in the second picture of the first post.

That is not "the graph of the complex number solution of X^2+1=0 in the coordinate system". The picture clearly says

The left side of f(x) shows that this is a function, and the right side shows that this is a quadratic function. So this curve is the graph of a quadratic function.

The curve in the second picture is correct, although not very smooth.

The curve does not intersect the horizontal axis because it is impossible for any value of x to make f(x) zero.

The curve intersects the vertical axis at the point (0, 1). Indeed, when x=0, f(x)=1.

This is a parabola.

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maychang posted on 2021-12-17 17:53 Let's go back to the curve shown in the second picture of the first post. That is not the "graph of the complex number solution of X^2+1=0 in the coordinate system", the picture...

Thank you very much. I feel that my foundation is too weak recently, so I bought some books and started from scratch according to the teachers' suggestions.

freebsder

You can't even crawl and you're trying to learn how to run. That's too big a step. Aren't you afraid of getting hurt?

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freebsder posted on 2021-12-20 09:37 You can't even crawl and you want to learn to run. The span is too big. Aren't you afraid of getting hurt?

Ha ha

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freebsder posted on 2021-12-20 09:37 You can't even crawl and you want to learn to run. The leap is too big. Aren't you afraid of getting hurt?

Prepare to learn, and then study the relationship between vacuum magnetic permeability and ether, publish a research report, and like de Broglie, inadvertently win a Nobel Prize