الرياضيات: النماذج والدوال والرياضيات العليا
ACT الموضوع 3 4:29 سرد باللغة الإنجليزية · ترجمة مدمجة بالإنجليزية + الصينية
فصول
النص الصوتي
A complex conjugate changes the imaginary sign.
共轭复数会改变虚部的符号。
The product of a plus b i times a minus b i equals a squared plus b squared, for real a and b.
对于实数a和b，(a加bi)乘以(a减bi)等于a的平方加b的平方。
Thus, two plus i divided by two minus i equals two plus i squared divided by five, which simplifies to three plus four i divided by five.
因此，(2加i)除以(2减i)等于(2加i)的平方除以5，即(3加4i)除以5。
The denominator is nonzero.
分母不为零。
Distinguish an exact value from its decimal approximation.
请区分精确值与其十进制近似值。
Each task gives its own data.
每个任务都有其自身的数据。
Do not copy the worked example’s numbers.
请勿照搬例题中的数值。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
Multiply both parts by one minus i.
分子分母同乘一减 i。
The numerator is three minus two i, times one minus i, which is three minus five i plus two i squared, or one minus five i.
分子是三减二 i 乘一减 i，等于三减五 i 加二 i 平方，也就是一减五 i。
The denominator is 2.
分母是二。
The answer is one half minus five halves i.
结果是二分之一减二分之五 i。
Multiplying back by one plus i returns three minus two i.
再乘以一加 i，就回到三减二 i。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息。
The fifth root of 32 is 2, so 32 to the power two fifths is 2 squared, which is 4.
三十二的五次方根是二，所以三十二的五分之二次方等于二的平方，也就是四。
The principal square root gives the absolute value of negative 7, which is 7.
主平方根给出负七的绝对值，即七。
For the equation, z squared equals negative 16 gives z equals 4 i or negative 4 i, both nonreal.
对于方程，z 的平方等于负十六，得到 z 等于四 i 或负四 i，两者都不是实数。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息作答。
Root 2 times root 2 equals 2, which is rational.
根号二乘根号二等于二，是有理数。
Root 2 times root 3 equals root 6, which is irrational.
根号二乘根号三等于根号六，是无理数。
Neither closure nor nonclosure for all products follows from the label irrational alone.
仅凭“无理数”这个标签，既推不出乘积总是封闭的，也推不出总是不封闭的。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请结合前几页的完整背景信息。
Root 50 equals 5 root 2, which is irrational, while root 50 times root 2 equals root 100, which is 10, a rational number.
根号五十等于五倍根号二，是无理数；而根号五十乘根号二等于根号一百，即十，是有理数。
32 to the power two fifths is the fifth root of 32, squared, which is 2 squared, or 4.
三十二的五分之二次方等于三十二的五次方根再平方，也就是二的平方，等于四。
And 2 to the power negative 3 is one over 2 cubed, which is one eighth.
二的负三次方等于二的三次方分之一，即八分之一。
The two irrational numbers sum to zero, which is rational; irrational numbers are not closed under addition.
这两个无理数相加等于零，零是有理数，所以无理数对加法不封闭。
These even-root products use nonnegative real radicands.
这些偶次根的乘积都使用非负实数被开方数。
Return to the task and explain why the method fits.
回到该任务，并解释为何此方法适用。
Original practice does not predict an official score.
原始练习无法预测正式成绩。
Complete required live or recorded evidence separately.
请单独完成所需的现场或录制证据。
Pause and test yourself. Cover the worked answer, rebuild the answer to the last example in your own words, and name one condition that would change it before you check.
暂停一下，自我检测：遮住示范答案，用自己的话重做最后一个例子的答案，并在核对之前说出一个会改变结论的条件。