The mathematician invented a complex number system.

那位数学家发明了一套复杂的数字系统。

A little messy? The Mandelbrot set of complex numbers is a little messy. This is chaos. Excuse me.

有一点凌乱？曼德尔布罗特集合才叫有一点凌乱，这简直是一团糟。不好意思。

In algebra, his work expanded our understanding of polynomial equations, opening new doors of exploration in complex numbers.

在代数面，他的工作扩展了我们对多程的理解，打开了探索复数的新门。

Complex numbers hard to remember, so systems have been created to simplify geocodes.

复杂的数字很难记， 已经创建了系统来简化地理编码。

More generally, they're related by a complex number.

更一般地，它们 通过复数相关联。

This was a significant milestone that connected the fields of algebra and complex numbers and showed the breadth and depth of Gauss's mathematical acumen.

这是一个重要的里程碑，连接了代数和复数领域，并展示了高斯数学敏锐度的广度和深度。

But then mathematicians defined the square root of negative one as a new number called i, opening up a whole new mathematical world of complex numbers.

但后来数学家们取 -1 的平根为一个叫 i 的新数字，在数学领域里，这为复杂数字打开了全新的世界。

We have strings numbers and boolean Numbers can be integers floats or complex numbers Here's the second question. You have this variable fruit set to Apple. What do you think?

我们有字符串数字和布尔数字可以是整数浮点数或复数这是第二个问题。您将这个变量 fruit 设置为 Apple。你怎么认为？

This letter is of a particular interest, partly because it's in code, a not very complex number for letter substitution, but also because it was written at the turning point of Napoleon's career.

这份书信是用密码写的，用的字母替换法也不难理解，而且书写这封信时，拿破仑正处在事业的转折点，这封信很有趣。