发布网友
发布时间：2024-10-21 22:58
共2个回答
热心网友
时间：2024-10-31 22:52
x^(1/3)定义域为0,正无穷。 不含负数。 负数开立方包含复数。
Given a number , the cube root of , denoted or ( to the 1/3 power), is a number such that . The cube root is therefore an nth root with . Every real number has a unique real cube root, and every nonzero complex number has three distinct cube roots.
The schoolbook definition of the cube root of a negative number is . However, extension of the cube root into the complex plane gives a branch cut along the negative real axis for the principal value of the cube root as illustrated above. By convention, "the" (principal) cube root is therefore a complex number with positive imaginary part. As a result, Mathematica and other symbolic algebra programs that return results valid over the entire complex plane therefore return complex results for . For example, in Mathematica, ComplexExpand[(-1)^(1/3)] gives the result .
When considering a positive real number , the Mathematica command CubeRoot[x], which is equivalent to Surd[x, 3], may be used to return the real cube root.
The cube root of a number can be computed using Newton's method by iteratively applying
热心网友
时间：2024-10-31 22:45
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