absolute value
absolute value — 名詞
1. in mathematics, the non-negative amount showing how far a real number is from ze
絕對值
數線上與零的距離
in mathematics, the non-negative amount showing how far a real number is from zero, without keeping the plus or minus sign.
Mira wrote that the absolute value of -9 is 9.
Mira 寫下 -9 的絕對值是 9。
pattern: the absolute value of + number
The worksheet asked Kofi to find the absolute value of 12.
講義要 Kofi 算出 12 的絕對值。
On the number line, both points had the same absolute value.
在數線上，那兩個點有相同的絕對值。
Bao checked the absolute value before comparing the two negative scores.
Bao 在比較兩個負分前，先查看它們的絕對值。
- modulus
more technical and often seen in textbooks, but it can mean the same thing for ordinary numbers
- distance from zero
explains the idea clearly, but it is a description rather than the formal term
文法句型
the absolute value of + number
find/calculate the absolute value of + number
用法筆記
Usually appears with numbers on a number line or in basic algebra. Distinguish from sense 2, which is used for complex numbers rather than ordinary signed numbers.
常見錯誤
2. in complex-number work, the positive length from zero to the point for that numb
複數模
複數點到原點的正長度
in complex-number work, the positive length from zero to the point for that number on the complex plane.
Hari found the absolute value of 3 + 4i by using a right triangle.
Hari 用直角三角形算出 3 + 4i 的複數模。
absolute value of + complex number
The graph showed the absolute value as the line from zero.
圖上把複數模畫成從原點伸出的那條線段。
idea: length from the origin
In class, Paloma said the absolute value of z was always positive.
課堂上，Paloma 說 z 的複數模一定是正數。
The quiz asked for the absolute value after students plotted the complex number.
小考要學生先畫出複數，再求它的複數模。
文法句型
the absolute value of + complex number
absolute value equals + number
用法筆記
Used in algebra and complex analysis when a complex number is shown as a point. Unlike sense 1, the value comes from the real and imaginary parts together, not from a single signed number.