محمد راضى سعد حسن

المزيد من المعرفة

العدد التخيلي والاعداد المركبة والعددان المترافقان

أولا العدد التخيلي: هو العدد الذي مربعه يساوي 1- ويرمز له بالرمز i وبالتالي يكون i²=-1.

وبصفة عامة

▪ i أس أي عدد مضاعف للعدد أربعة يكون الناتج يساوي الواحد الصحيح

▪ i أس عدد موجب نقوم بطرح المضاعف الاقل للعدد أربعة

▪ i أس عدد سالب نقوم بجمع المضاعف الاكبر للعدد أربعة

ثانيا العدد المركب: هو عدد مكون من عددين احدهما حقيقي والاخر تخيلي وتكون صورة هذا العدد هي (a+b i) حيث يسمى a بالعدد الحقيقي بينما b يسمى بالجزء التخيلي.

ملحوظات هامة

▪ كل عدد حقيقي اصله عدد مركب حده التخيلي يساوي صفر

أى أن مجموعة الاعداد الحقيقة جزئية من مجموعة الاعداد المركبة.

▪ يرمز لمجموعة الاعداد المركبة بالرمز C.

▪ يتساوى العددان المركبان إذا وفقط تساوى العدد الحقيقي للعدد المركب الاول بالعدد الحقيقي للعدد المركب الثاني و تساوى الجزء التخيلي للعدد المركب الاول بالجزء التخيلي للعدد المركب الثاني.

▪ عند جمع أو طرح الاعداد المركبة نجمع أو نطرح الحقيقي مع الحقيقي والتخيلي مع التخيلي.

▪ عند ضرب عددين مركبين نقوم بالضرب كأننا نضرب قوسين.

ثالثا العددان المترافقان: هما عددان مشتركان في العدد الحقيقي ومختلفان في اشارة الجزء التخيلي.

ملحوظات هامة

▪ مرافق العدد 5+2i هو 5+2i-.

▪ مرافق العدد 10 هو 10.

▪ حاصل ضرب وجمع عددين مترافقين دائما عدد حقيقي.

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