题目
On a sketch of an Argand diagram shade the region whose points represent complex numbers satisfying the inequalities , and .
题目中文翻译
在阿尔冈图的草图上,用阴影表示由满足不等式 、 和 的复数 所对应的点组成的区域。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程;仅给出计算器答案而没有过程,不予评分。除非题目另有精度要求,非精确数值答案保留 3 位有效数字,以度为单位的角度保留 1 位小数。
解答
解法一
思路
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三个条件分别给出闭圆盘、直线 右侧,以及辐角介于 与 的扇形。涂色须同时满足三个条件。
答题过程
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Write . Draw the circle , the vertical line , and the ray from the origin into the first quadrant.
Shade the points satisfying
Equivalently, shade the part inside the circle, to the right of , above the real axis and above the ray . Include the boundaries, except the origin where the argument is undefined.