Complex Numbers复数
A complex number is a number with a real and an imaginary part, usually expressed in cartesian form 复数是一个具有实部和虚部的数，通常用笛卡尔形式表示
 The polar form can also be expressed in terms of trigonometric functions using the Euler relationship 极坐标形式也可以用三角函数表示，使用欧拉关系
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Euler Relationship欧拉关系
The trigonometric functions are related to a complex exponential by the Euler relationship 三角函数与复指数之间存在欧拉关系
 From these relationships the trig functions can be expressed in terms of the complex exponential: 从这些关系可以将三角函数用复指数表示为：
 This relationship is useful for expressing complex numbers in polar form, as well as many other applications. 这种关系在用极坐标表示复数以及其他许多应用中都非常有用。
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Polar Form, Complex Numbers复数的极坐标形式
The standard form of a complex number is 复数的标准形式是
but this can be shown to be equivalent to the form 但可以证明这与另一种形式等价
 which is called the polar form of a complex number. The equivalence can be shown by using the Euler relationship for complex exponentials. 这被称为复数的极坐标形式。可以通过使用复指数的欧拉关系来证明其等价性。
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