论文部分内容阅读
解:由z~2=z两边求模,得|z|~2=|z|=|z||z|=1(|z|≠0)。再用Z(≠0)乘方程两边得z~3=z·z=1。这是高中代数复数中的一道习题: 已知z是虚数,解方程z~2=z 此题的解法通常利用复数的代数式化为二元方程组分别求z的实部和虚部,也有化为三角式求z的模及其辐角的。但都不如以下解法简便。 32
Solution: By z~2=z on both sides, get |z|~2=|z|=|z||z|=1(|z|≠0). Then use Z(≠0) to multiply equations on both sides to get z~3=z·z=1. This is an exercise in high school algebraic plurals: Knowing that z is an imaginary number and solving the equation z~2=z The solution to this problem is usually to use algebraic expressions of complex numbers to find the real and imaginary parts of z separately for the system of binary equations. Finding the z-modulus and its arguments for the triangle. However, it is not as simple as the following solution. 32