九一年上海高考数学试题的第25题,是值得我们化费一点笔墨探讨的考题。其(1)是: 设复数z的幅角为θ(0≤θ<π),且满足等式|z-i|=1。求复数x~2-zi的幅角(用含θ的式子表示)其中i为虚数单位。试题的解答者为该小题仅仅给出了一种解法,并且运算量不小。笔者试图结合命题的几何意义,再给出一种简便解法。另外,笔者认 The twenty-fifth question in the 91st Shanghai Mathematics Exam Questions is a question worthy of our consideration. Its (1) is: Let the argument of the complex number z be θ (0≤θ<π), and satisfy the equation |z-i|=1. Find the argument of the complex number x~2-zi (represented by the expression with θ) where i is the imaginary unit. The solver of the question only gave a solution to the question, and the amount of calculation was not small. The author tries to combine the geometric meaning of the proposition and give a simple solution. In addition, the author believes