# max and min complex number

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ElizabethR 2016 年 6 月 7 日
コメント済み: ElizabethR 2016 年 6 月 14 日
i have set that contain complex number, then i get the greatest value using max function and get the smallest value using min function. For example the max value is -0.0115230+0.0474206i and the minimum value is 0.0026796 + 0.0006868i But if i give this command -0.0115230+0.0474206i > 0.0026796 + 0.0006868i it get the result ans=0. So, how did it happen ? should the result is ans=1 ?? please help. i am very confused

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### 採用された回答

Guillaume 2016 年 6 月 7 日
It can be proven that complex numbers cannot be ordered (under the definition of an ordered field). That means that you cannot compare complex numbers.
As per the documentation, < (and co.) only compare the real part of a number, whereas min returns the complex number with the smallest magnitude.
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Guillaume 2016 年 6 月 14 日
Complex numbers are the same as points on a 2D plane. Given a set of points in a plane, can you tell which is the minimum and which is the maximum? No, the concept does not make sense. Same for complex numbers.
Similarly, given a set of points, can you tell if another point is in the range of these points? Well, first you have to define what you mean by the range of a set of points. Until you do that, we can't help you.
Possibly, you can define a point in range of a set of point if it is within the convex hull of the set, but only you can decide that.
ElizabethR 2016 年 6 月 14 日
yes, thanks for your explanation. Now i am understand about complex number. thank you so much Guillaume.

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### その他の回答 (2 件)

Azzi Abdelmalek 2016 年 6 月 7 日

If x1=1.1+2*i and x2=1+2.1*i What is the smallest number ? You can't compare two complex numbers, you can compare their modulus
abs(x1)>abs(x2)
I think max and min function, in your case, are finding the max and min of abs(your_array)
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Guillaume 2016 年 6 月 9 日
"If you wish to create an order then you can use the magnitude."
You can, but that ordering is not compatible with addition and multiplication. So, with that ordering, if you have
z1 < z2
You cannot assume that
z1 + c < z2 + c %c a complex constant
z1 * c < z2 * c, with c > 0 a complex constant
ElizabethR 2016 年 6 月 14 日
hi Guillaume, thank you so much for your answare and explanation. Yes, now i am understand. Thank you. May i ask once again ? whether you have reference ( ebook ) about complex number ? so i can make strong argument in my task about complex number. God Bless You. sorry for my bad english

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Iain 2016 年 6 月 7 日
Max is calculating the absolute value, and then taking the maximum value, despite being negative.
Greater than is taking the value farthest from negative infinity.
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Torsten 2016 年 6 月 9 日

@eliz, I asked because your question had already been answered several times and it seemed to me you were not satisfied with these responses. So my guess was that you tried to ask something different, something we did not yet understand.
Best wishes
Torsten.
ElizabethR 2016 年 6 月 14 日

hi Torsten. oohhh I am Sorry, May be it became misunderstand, it not mean i am not satisfied with the answare, but, i confused so i ask again. But thank you so much. May i ask once again ? whether you have reference ( ebook ) about complex number ? so i can make strong argument in my task about complex number. God Bless You. sorry for my bad english

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