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由复数三角形式的乘除法则我们知道复数的辐角有如下性质:两个复数相乘,积的辐角等于各复数辐角的和;两个复数相除,商的辐角等于被除数的辐角减去除数的辐角所得的差。本文拟通过例题,介绍复数辐角的性质在反三角函数中的应用。一、利用复数辐角的性质进行反三角函数和差的运算先将反三角函数的和差转化为复数积商的辐角,然后求出复数积商的辐角在反三角函数值域内的辐角。例1 计算
From the multiplicity and division method of complex triangles, we know that the arguments of complex numbers have the following properties: the multiplication of two complex numbers, the argument of the product is equal to the sum of the arguments of the complex numbers, the division of two complex numbers, and the argument of the quotient is equal to the argument of the divisor. The difference obtained by subtracting the projection angle of the removal number. This article intends to introduce the application of complex arguments in inverse trigonometric functions through examples. First, use the nature of complex arguments to perform inverse trigonometric functions and difference operations. First, convert the sum of the inverse trigonometric functions into the argument of the complex product quotient, and then find the radius of the argument of the complex product quotient in the range of the inverse trigonometric function. angle. Example 1 Calculation