Cube root polar angle by three in order to define a cube root. With this definition, the principal cube root of a negative number is a complex number, and for instance will not be −2, but rather . This difficulty can also be solved by considering the cube root as a multivalued function: if we write the original complex number "x" in three equivalent forms, namely The principal complex cube roots of these three forms are then respectively Unless , these three complex numbers are distinct, even though the three representations of "x" were equivalent. For example, may then be calculated to
Cube root this required the construction, now known to be impossible, of the length . A method for extracting cube roots appears in "The Nine Chapters on the Mathematical Art", a Chinese mathematical text compiled around the 2nd century BCE and commented on by Liu Hui in the 3rd century CE. The Greek mathematician Hero of Alexandria devised a method for calculating cube roots in the 1st century CE. His formula is again mentioned by Eutokios in a commentary on Archimedes. In 499 CE Aryabhata, a mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave a method for finding