本研究旨在探討高一學生於「複數與複數平面」單元教學完畢後，解題時發生錯誤的主要類型，並探討發生錯誤的原因，再根據這些錯誤的原因，設計補救教學課程，以進行補救教學活動，並分析補救教學活動的成效。 根據本研究，學生於「複數與複數平面」單元解題主要錯誤類型有下列十一種：對複數的定義了解不清、不知二根式乘除的運算規則、不熟悉i的次n方或不具「級數」觀念無法順利利用 乘冪的特殊性質、作複數的四則運算時易發生錯誤、不知複數絕對值的意義或觀念仍停留在國中「負的變正的，正的還是正的」的錯誤觀念、不清楚共軛複數的定義或共軛複數與複數絕對值產生混淆、不會利用複數絕對值的運算性質、無法將複數正確地對應到複數平面上、平面幾何能力不足、尚未建立複數概念、習慣以整數思考。發生錯誤的主要因素有：定義不清，似是而非、受直觀影響，產生錯誤類推、無法將複數與複數平面連結、先備知識不足。 補救教學成效方面：空白率不論由整份試卷或個別試題做檢定，均呈現明顯下降、答對率以整體學生來看，大部分試題答對率均上升，以高低分組來看，無論是高分組或低分組學生，成績均明顯改善。保留效果以整體學生來看，答對率並沒有顯著差異，全體學生後測與延後測成績呈高度正相關。特別針對低分組學生做檢定，發現低分組學生的學習保留得很好，後測與延後測答題差異並不顯著。此外，學生普遍認為以PowerPoint 與 GSP 為工具的補救教學，學習內容與教材更能吸引學生的注意，增進學生的學習成效，因此學生對補救教學大多抱持著正面的看法。 / The research aims to explore the main error types of first grader’s in a senior high school when solving the unit of complex number and complex plane after the instruction, including the possible reasons of their errors. The course designs of the remedial instructions are followed according to those reasons. At the end of this study, some analyses of the effects of remedial instruction activities are provided. In this study, there are eleven main error types from the first graders when proceeding to do the unit of complex number and complex plane : vague understanding about the definition of complex number; lacking necessary knowledge for the operation rules with the multiplication and division of two radicals; unfamiliar with handling the power of i and sum of the them; constantly making mistakes when doing the fundamental operations of arithmetic with complex number; confusing the meaning or conception concerning the absolute value of complex number under the false ideas existed in junior high about “A negative becomes a positive , and a positive is still a positive ”; not knowing the definition of conjugate complex number or confusing conjugate complex number with the absolute value of complex number; incapable of using the idea of operating the absolute value of complex number; failing to relate complex number to complex plane; inability in plane geometry; unable to construct the concept of complex number; habitual thinking with integer. The primary factors of making the above errors, according to this research, are as follows: ambiguous definition; paradoxical; influenced by instinct; making false analogy; failing to effectively connect complex number with complex plane; lacking prerequisite knowledge. As for the results of this remedial teaching, the rate of blank in students’ answer sheets, regardless of the whole test sheets or individual tests, has obviously decreased; the learners’ rate of accuracy as a whole is mostly higher; the improvement of grades, both in the brilliant group and in the poor group, is significantly improved; the effect of retention, in view of the whole participants’ rate of accuracy, varies insignificantly; more important, the results of students’ post-tests and postponed post-tests are in highly positive correlation. In testing the poor group, we find their retention of learning excellent. The variations of answers in the post-tests and postponed post-tests are not significant. Besides, most learners pay much attention to the contents and materials of employing Power Point and GSP and consider them as useful tools in the remedial teaching. In conclusion, the participants make great progress under this experiment. Therefore, most learners take positive perspectives from the remedial instruction.