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初等数学的研究对象是数与形,两者之间的互相渗透关系在高中教材复数一章有着充分的反映。1986年高考数学(文科)试题关于复数的考题四,具有紧扣教材,基础性强;形数关系体现突出,灵巧多变的特点。原题求满足方程|Z+3-3~(1/2)i|=3~(1/2)的辐角主值最小的复数Z。本题涉及的概念较多,诸如复数、复数的摸、复数的辐角及辐角的主值等等。从卷面所反映的情况看,大多数是白卷或错答的,只有少数考生解答正确。从解答正确的考生看,他们不仅对有关概念有正确的理解,娴熟复数的种种表示和几何意义,更主要的是他们在题目的条件和要求之间能建立
The research object of elementary mathematics is number and shape. The mutual penetration between them has been fully reflected in the plural chapters of high school textbooks. The 1986 college entrance examination mathematics (arts) examination questions on the plural number of questions, with closely linked teaching materials, strong foundation; the relationship between the shape of the number of outstanding, flexible and changeable features. The original question finds the complex number Z with the smallest principal value of the argument satisfying the equation |Z+3-3~(1/2)i|=3~(1/2). This concept involves more concepts, such as the complex number, the complex number of the complex, the complex angle and the main value of the argument, and so on. Judging from the situation reflected in the reels, most of them are white papers or wrong answers, and only a few candidates answered correctly. From the answer to correct candidates, they not only have a correct understanding of the concepts, they are familiar with the various representations and geometric meanings of plural numbers, and more importantly, they can establish the conditions and requirements of the questions.