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根据复数的初等性质和运算法则,使我们能充分地利用复数去研究三角中的问题。例如,利用棣莫佛定理能够推出倍角的正余弦公式,利用复数的乘法和乘方法则可以推出正弦和余弦的加法定理等等。此外,利用复数可以证明三角中的一些重要公式、定理,还可以证明三角恒等式和计算三角和等问题。本文的目的是利用复数解三角中的一些问题。为了方便起见,我们给复数以简便记号,这种记号被称作Francais记号,1813年由他所创,后来被柯西采用过。
Based on the elementary nature of the plural and the algorithm, we can make full use of the complex number to study the problems in the triangle. For example, using the Moore’s theorem to derive the sine and cosine formula of the double angle, using the method of multiplication and multiplication of plurals, the addition theorem of sine and cosine can be derived. In addition, using the complex number can prove some important formulas and theorems in the triangle, and can also prove the trigonometric identities and the calculation of triangular sums. The purpose of this article is to use some of the problems in the solution of complex triangles. For the sake of convenience, we give the plural number a simple notation. This notation is called the Francais notation. It was created by him in 1813 and later adopted by Cauchy.