[{"_1":2,"_321":-5,"_322":-5},"loaderData",{"_3":4,"_28":29,"_320":-5},"root",{"_5":6,"_24":25,"_26":27},"allTopics",[7],{"_8":9,"_10":11,"_12":13,"_14":15,"_16":17},"id",2,"title","قدرات عامة","slug","قدرات-عامة","description","اختبار القدرات للمرحلة الثانوية هو اختبار يقيس القدرة على الفهم والتطبيق والاستدلال والتحليل لدى الطالب من خلال اللغة والرياضيات، و معرفة قابلية الطالب للتعلم","metadata",{"_18":19,"_20":19,"_21":19,"_22":19,"_23":19},"support_dynamic_study_plan",true,"study_plan_based_on_section_level","placement_test_based_on_section_level","study_plan_based_on_topic_level","placement_test_based_on_topic_level","whiteLabelData",{},"isWhitelabeled",false,"routes/_visitor.question.$slug",{"_30":31,"_99":100,"_301":302,"_314":315,"_316":27,"_317":32,"_318":319},"loaderQuestion",{"_8":32,"_33":34,"_35":36,"_10":37,"_12":38,"_39":40,"_41":42,"_43":44,"_45":46,"_47":46,"_48":27,"_49":27,"_50":-5,"_51":52,"_70":71,"_76":77,"_81":82,"_83":27,"_84":-5,"_85":86,"_87":88,"_89":90,"_91":92,"_93":19,"_56":94,"_95":96,"_97":98},69207,"type","MULTIPLE_CHOICE","text","أكتب العدد المركب \\ltr{2 + 2i \\sqrt{3}} بالصورة القطبية","أكتب العدد المركب 2 + 2i √(3) بالصورة القطبية A)4(cos120^∘+ i sin120^∘) B)4(cos60^∘+ i sin60^∘) C)4(cos300^∘+ i sin300^∘) D)4(cos240^∘+ i sin60^∘) ","69207-أكتب-العدد-المركب-}-بالصورة-القطبية","order",68,"unit_id",58,"topic_id",3,"comparison_value1","","comparison_value2","has_text_explanation","has_video_explanation","question_group","question_options",[53,58,62,66],{"_8":54,"_35":55,"_56":57},258477,"\\ltr{4(\\cos 120^\\circ + i \\sin 120^\\circ)}","renderedText"," $\"\"/$ ",{"_8":59,"_35":60,"_56":61},258478,"\\ltr{4(\\cos 60^\\circ + i \\sin 60^\\circ)}"," $\"\"/$ ",{"_8":63,"_35":64,"_56":65},258479,"\\ltr{4(\\cos 300^\\circ + i \\sin 300^\\circ)}"," $\"\"/$ ",{"_8":67,"_35":68,"_56":69},258480,"\\ltr{4(\\cos 240^\\circ + i \\sin 60^\\circ)}"," $\"\"/$ ","previous_question",{"_8":72,"_33":34,"_35":73,"_12":74,"_10":-5,"_45":46,"_47":46,"_48":-5,"_49":-5,"_41":-5,"_75":-5,"_43":-5,"_50":-5},69205,"ما مركز الدائرة من المعادلة \\ltr{r = 2(\\cos \\theta - 2 \\sin \\theta) + \\frac{4}{r}}","69205-ما-مركز-الدائرة-من-المعادلة-{r","section_id","next_question",{"_8":78,"_33":34,"_35":79,"_12":80,"_10":-5,"_45":46,"_47":46,"_48":-5,"_49":-5,"_41":-5,"_75":-5,"_43":-5,"_50":-5},69208,"المعادلة الديكارتية \\ltr{y = 2} بالصيغـة القطبية هي..","69208-المعادلة-الديكارتية-بالصيغـة-القطبية-هي","user_video_explanations",[],"has_custom_text_explanation","text_explanation_teaser","total_questions_number",86,"unitTitle","الإحداثيات القطبية","sectionTitle","الرياضيات","sectionId",35,"canExpandImages","أكتب العدد المركب $\"\"/$ بالصورة القطبية","encodedPrevQuestionSlug","69205-%D9%85%D8%A7-%D9%85%D8%B1%D9%83%D8%B2-%D8%A7%D9%84%D8%AF%D8%A7%D8%A6%D8%B1%D8%A9-%D9%85%D9%86-%D8%A7%D9%84%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9-%7Br","encodedNextQuestionSlug","69208-%D8%A7%D9%84%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9-%D8%A7%D9%84%D8%AF%D9%8A%D9%83%D8%A7%D8%B1%D8%AA%D9%8A%D8%A9-%D8%A8%D8%A7%D9%84%D8%B5%D9%8A%D8%BA%D9%80%D8%A9-%D8%A7%D9%84%D9%82%D8%B7%D8%A8%D9%8A%D8%A9-%D9%87%D9%8A","relatedQuestions",[101,121,141,161,181,201,221,241,261,281],{"_8":72,"_33":34,"_35":73,"_12":96,"_10":102,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":46,"_47":46,"_48":27,"_49":27,"_50":-5,"_51":104,"_81":117,"_83":27,"_118":27,"_119":-5,"_56":120},"ما مركز الدائرة من المعادلة r = 2(cosθ- 2 sinθ) + 4/r A)(1, 2) B)(1, -2) C)(-1, 2) D)(-1, -2) ","unit_name",[105,108,111,114],{"_8":106,"_35":107},258469,"\\ltr{(1, 2)}",{"_8":109,"_35":110},258470,"\\ltr{(1, -2)}",{"_8":112,"_35":113},258471,"\\ltr{(-1, 2)}",{"_8":115,"_35":116},258472,"\\ltr{(-1, -2)}",[],"is_all_explanations_deleted","contents_tags_ids","ما مركز الدائرة من المعادلة $\"\"/$ ",{"_8":122,"_33":34,"_35":123,"_12":124,"_10":125,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":46,"_47":46,"_48":27,"_49":27,"_50":-5,"_51":126,"_81":139,"_83":27,"_118":27,"_119":-5,"_56":140},69203,"إذا كان \\ltr{z_1=2\\left(\\cos\\frac{\\pi}{6}+i\\sin\\frac{\\pi}{6}\\right)} ، \\ltr{z_2=5\\left(\\cos\\frac{\\pi}{3}+i\\sin\\frac{\\pi}{3}\\right)} ، فما حاصل ضرب \\ltr{z_1z_2}؟","69203-%D8%A5%D8%B0%D8%A7-%D9%83%D8%A7%D9%86-%7B6%7D%2Bi%7B6%7D)%7D-%7B3%7D%2Bi%7B3%7D)%7D-%D9%81%D9%85%D8%A7-%D8%AD%D8%A7%D8%B5%D9%84-%D8%B6%D8%B1%D8%A8-%7B2%7D%2Bi%7B2%7D)%7D-%7B2%7D-i%7B2%7D)%7D-%7B18%7D%2Bi%7B18%7D)%7D-%7B18%7D-i%7B18","إذا كان z_1=2(cosπ/6+isinπ/6) ، z_2=5(cosπ/3+isinπ/3) ، فما حاصل ضرب z_1z_2؟ A)10(cosπ/2+isinπ/2) B)10(cosπ/2-isinπ/2) C)10(cos^2π^2/18+isinπ^2/18) D)10(cos^2π^2/18-isinπ^2/18) ",[127,130,133,136],{"_8":128,"_35":129},258461,"\\ltr{10\\left(\\cos\\frac{\\pi}{2}+i\\sin\\frac{\\pi}{2}\\right)}",{"_8":131,"_35":132},258462,"\\ltr{10\\left(\\cos\\frac{\\pi}{2}-i\\sin\\frac{\\pi}{2}\\right)}",{"_8":134,"_35":135},258463,"\\ltr{10(\\cos^2\\frac{\\pi^2}{18}+i\\sin\\frac{\\pi^2}{18})}",{"_8":137,"_35":138},258464,"\\ltr{10(\\cos^2\\frac{\\pi^2}{18}-i\\sin\\frac{\\pi^2}{18})}",[],"إذا كان $\"\"/$ ، $\"\"/$ ، فما حاصل ضرب $\"\"/$ ؟",{"_8":142,"_33":34,"_35":143,"_12":144,"_10":145,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":46,"_47":46,"_48":27,"_49":27,"_50":-5,"_51":146,"_81":159,"_83":27,"_118":27,"_119":-5,"_56":160},69202,"حول المعادلة التالية للصورة الديكارتية \\ltr{r = \\frac{7}{\\sec{\\theta}}}","69202-%D8%AD%D9%88%D9%84-%D8%A7%D9%84%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9-%D8%A7%D9%84%D8%AA%D8%A7%D9%84%D9%8A%D8%A9-%D9%84%D9%84%D8%B5%D9%88%D8%B1%D8%A9-%D8%A7%D9%84%D8%AF%D9%8A%D9%83%D8%A7%D8%B1%D8%AA%D9%8A%D8%A9","حول المعادلة التالية للصورة الديكارتية r = 7/θ A)x^2 + y^2 = 7x B)x^2 + y^2 = 49 C)x^2 - y^2 = 49 D)x^2 + y^2 = 7y ",[147,150,153,156],{"_8":148,"_35":149},258457,"\\ltr{x^2 + y^2 = 7x}",{"_8":151,"_35":152},258458,"\\ltr{x^2 + y^2 = 49}",{"_8":154,"_35":155},258459,"\\ltr{x^2 - y^2 = 49}",{"_8":157,"_35":158},258460,"\\ltr{x^2 + y^2 = 7y}",[],"حول المعادلة التالية للصورة الديكارتية $\"\"/$ ",{"_8":162,"_33":34,"_35":163,"_12":164,"_10":165,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":46,"_47":46,"_48":27,"_49":27,"_50":-5,"_51":166,"_81":179,"_83":27,"_118":27,"_119":-5,"_56":180},69201,"إحداثيات النقطة T الموضحة في الشكل هي....\n11f13d72_3b64_216d_bf57_4dd6c1c41d48_00","69201-%D8%A5%D8%AD%D8%AF%D8%A7%D8%AB%D9%8A%D8%A7%D8%AA-%D8%A7%D9%84%D9%86%D9%82%D8%B7%D8%A9-T-%D8%A7%D9%84%D9%85%D9%88%D8%B6%D8%AD%D8%A9-%D9%81%D9%8A-%D8%A7%D9%84%D8%B4%D9%83%D9%84-%D9%87%D9%8A-%7B5%7D)%7D-%7B4%7D)%7D-%7B3%7D)%7D-%7B3","إحداثيات النقطة T الموضحة في الشكل هي.... A)(6, 3π/5) B)(6, 3π/4) C)(6, 4π/3) D)(6, 5π/3) ",[167,170,173,176],{"_8":168,"_35":169},258453,"\\ltr{(6, \\frac{3\\pi}{5})}",{"_8":171,"_35":172},258454,"\\ltr{(6, \\frac{3\\pi}{4})}",{"_8":174,"_35":175},258455,"\\ltr{(6, \\frac{4\\pi}{3})}",{"_8":177,"_35":178},258456,"\\ltr{(6, \\frac{5\\pi}{3})}",[],"إحداثيات النقطة T الموضحة في الشكل هي.... $\"\"$ ",{"_8":182,"_33":34,"_35":183,"_12":184,"_10":185,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":46,"_47":46,"_48":27,"_49":27,"_50":-5,"_51":186,"_81":199,"_83":27,"_118":27,"_119":-5,"_56":200},69200,"أي العبارات التالية تمثل المتجه في الصورة الديكارتية؟\n11f13d71_e37f_852b_bf57_7bc2eabf474c_00","69200-%D8%A3%D9%8A-%D8%A7%D9%84%D8%B9%D8%A8%D8%A7%D8%B1%D8%A7%D8%AA-%D8%A7%D9%84%D8%AA%D8%A7%D9%84%D9%8A%D8%A9-%D8%AA%D9%85%D8%AB%D9%84-%D8%A7%D9%84%D9%85%D8%AA%D8%AC%D9%87-%D9%81%D9%8A-%D8%A7%D9%84%D8%B5%D9%88%D8%B1%D8%A9-%D8%A7%D9%84%D8%AF%D9%8A%D9%83%D8%A7%D8%B1%D8%AA%D9%8A%D8%A9","أي العبارات التالية تمثل المتجه في الصورة الديكارتية؟ A)(-3, 3√(3)) B)(-3, -3√(3)) C)(3, -3√(3)) D)(3, 3√(3)) ",[187,190,193,196],{"_8":188,"_35":189},258449,"\\ltr{(-3, 3\\sqrt{3})}",{"_8":191,"_35":192},258450,"\\ltr{(-3, -3\\sqrt{3})}",{"_8":194,"_35":195},258451,"\\ltr{(3, -3\\sqrt{3})}",{"_8":197,"_35":198},258452,"\\ltr{(3, 3\\sqrt{3})}",[],"أي العبارات التالية تمثل المتجه في الصورة الديكارتية؟ $\"\"$ ",{"_8":202,"_33":34,"_35":203,"_12":204,"_10":205,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":46,"_47":46,"_48":27,"_49":19,"_50":-5,"_51":206,"_81":219,"_83":27,"_118":27,"_119":-5,"_56":220},56947,"ما احداثيات النقطة A\n11f099d4_c986_1804_9c99_3b1faab92302_00","56947-%D9%85%D8%A7-%D8%A7%D8%AD%D8%AF%D8%A7%D8%AB%D9%8A%D8%A7%D8%AA-%D8%A7%D9%84%D9%86%D9%82%D8%B7%D8%A9-A-%7B3%7D)%7D-%7B3%7D)%7D-%7B3%7D)%7D-%7B3","ما احداثيات النقطة A A)(-3, 2π/3) B)(3, 2π/3) C)(-3, -2π/3) D)(3, -2π/3) ",[207,210,213,216],{"_8":208,"_35":209},219238,"\\ltr{(-3, \\frac{2\\pi}{3})}",{"_8":211,"_35":212},219239,"\\ltr{(3, \\frac{2\\pi}{3})}",{"_8":214,"_35":215},219240,"\\ltr{(-3, -\\frac{2\\pi}{3})}",{"_8":217,"_35":218},219241,"\\ltr{(3, -\\frac{2\\pi}{3})}",[],"ما احداثيات النقطة A $\"\"$ ",{"_8":222,"_33":34,"_35":223,"_12":224,"_10":225,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":-5,"_47":-5,"_48":27,"_49":19,"_50":-5,"_51":226,"_81":239,"_83":27,"_118":27,"_119":-5,"_56":240},56686,"المستقيم \\ltr{y = -2} يمر بالنقطتين:","56686-%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%82%D9%8A%D9%85-%D9%8A%D9%85%D8%B1-%D8%A8%D8%A7%D9%84%D9%86%D9%82%D8%B7%D8%AA%D9%8A%D9%86","المستقيم y = -2 يمر بالنقطتين: A)(-2,7) , (-2,1) B)(-2,2) , (7,2) C)(4,7) , (4,-7) D)(4,-2) ,(-2,-2) ",[227,230,233,236],{"_8":228,"_35":229},218359,"\\ltr{(-2,7) , (-2,1)}",{"_8":231,"_35":232},218360,"\\ltr{(-2,2) , (7,2)}",{"_8":234,"_35":235},218361,"\\ltr{(4,7) , (4,-7)}",{"_8":237,"_35":238},218362,"\\ltr{(4,-2) ,(-2,-2) }",[],"المستقيم $\"\"/$ يمر بالنقطتين:",{"_8":242,"_33":34,"_35":243,"_12":244,"_10":245,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":-5,"_47":-5,"_48":27,"_49":19,"_50":-5,"_51":246,"_81":259,"_83":27,"_118":27,"_119":-5,"_56":260},56146,"إذا رصد رادار صاروخين إحداثياتهما \\ltr{(2,30^\\circ)} و \\ltr{(6,90^\\circ)}، اوجد المسافة بين الرادار والصاروخ الثاني اذا كان يقع في منتصف المسافة بين الصاروخ الأول والرادار","56146-%D8%A5%D8%B0%D8%A7-%D8%B1%D8%B5%D8%AF-%D8%B1%D8%A7%D8%AF%D8%A7%D8%B1-%D8%B5%D8%A7%D8%B1%D9%88%D8%AE%D9%8A%D9%86-%D8%A5%D8%AD%D8%AF%D8%A7%D8%AB%D9%8A%D8%A7%D8%AA%D9%87%D9%85%D8%A7-%D9%88-%D8%A7%D9%88%D8%AC%D8%AF-%D8%A7%D9%84%D9%85%D8%B3%D8%A7%D9%81%D8%A9-%D8%A8%D9%8A%D9%86-%D8%A7%D9%84%D8%B1%D8%A7%D8%AF%D8%A7%D8%B1-%D9%88%D8%A7%D9%84%D8%B5%D8%A7%D8%B1%D9%88%D8%AE-%D8%A7%D9%84%D8%AB%D8%A7%D9%86%D9%8A-%D8%A7%D8%B0%D8%A7-%D9%83%D8%A7%D9%86-%D9%8A%D9%82%D8%B9-%D9%81%D9%8A-%D9%85%D9%86%D8%AA%D8%B5%D9%81-%D8%A7%D9%84%D9%85%D8%B3%D8%A7%D9%81%D8%A9-%D8%A8%D9%8A%D9%86-%D8%A7%D9%84%D8%B5%D8%A7%D8%B1%D9%88%D8%AE-%D8%A7%D9%84%D8%A3%D9%88%D9%84-%D9%88%D8%A7%D9%84%D8%B1%D8%A7%D8%AF%D8%A7%D8%B1","إذا رصد رادار صاروخين إحداثياتهما (2,30^∘) و (6,90^∘)، اوجد المسافة بين الرادار والصاروخ الثاني اذا كان يقع في منتصف المسافة بين الصاروخ الأول والرادار A)2√(7) B)4√(7) C)14√(2) D)3√(4) ",[247,250,253,256],{"_8":248,"_35":249},216727,"\\ltr{2\\sqrt{7}}",{"_8":251,"_35":252},216728,"\\ltr{4\\sqrt{7}}",{"_8":254,"_35":255},216729,"\\ltr{14\\sqrt{2}}",{"_8":257,"_35":258},216730,"\\ltr{3\\sqrt{4}}",[],"إذا رصد رادار صاروخين إحداثياتهما $\"\"/$ و $\"\"/$ ، اوجد المسافة بين الرادار والصاروخ الثاني اذا كان يقع في منتصف المسافة بين الصاروخ الأول والرادار",{"_8":262,"_33":34,"_35":263,"_12":264,"_10":265,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":-5,"_47":-5,"_48":27,"_49":27,"_50":-5,"_51":266,"_81":279,"_83":27,"_118":27,"_119":-5,"_56":280},56145,"عجلة ماء أدنى نقطة فيها (0,0) وأعلى نقطة (0,30°)، ما المعادلة القطبية التي تمثل العجلة؟\n11f09092_33d5_57f6_ac3f_71f9f41c1d56_00","56145-%D8%B9%D8%AC%D9%84%D8%A9-%D9%85%D8%A7%D8%A1-%D8%A3%D8%AF%D9%86%D9%89-%D9%86%D9%82%D8%B7%D8%A9-%D9%81%D9%8A%D9%87%D8%A7-(0%2C0)-%D9%88%D8%A3%D8%B9%D9%84%D9%89-%D9%86%D9%82%D8%B7%D8%A9-(0%2C30%C2%B0)-%D9%85%D8%A7-%D8%A7%D9%84%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9-%D8%A7%D9%84%D9%82%D8%B7%D8%A8%D9%8A%D8%A9-%D8%A7%D9%84%D8%AA%D9%8A-%D8%AA%D9%85%D8%AB%D9%84-%D8%A7%D9%84%D8%B9%D8%AC%D9%84%D8%A9","عجلة ماء أدنى نقطة فيها (0,0) وأعلى نقطة (0,30°)، ما المعادلة القطبية التي تمثل العجلة؟ A)r = cos30 B)r = cos15 C)r=30 sin θ D)r = sin15 ",[267,270,273,276],{"_8":268,"_35":269},216723,"\\ltr{r = cos30}",{"_8":271,"_35":272},216724,"\\ltr{r = cos15}",{"_8":274,"_35":275},216725,"\\ltr{r=30\\;sin\\;\\theta\\;}",{"_8":277,"_35":278},216726,"\\ltr{r = sin15}",[],"عجلة ماء أدنى نقطة فيها (0,0) وأعلى نقطة (0,30°)، ما المعادلة القطبية التي تمثل العجلة؟ $\"\"$ ",{"_8":282,"_33":34,"_35":283,"_12":284,"_10":285,"_41":42,"_103":-5,"_43":44,"_75":92,"_45":-5,"_47":-5,"_48":27,"_49":19,"_50":-5,"_51":286,"_81":299,"_83":27,"_118":27,"_119":-5,"_56":300},56142,"ما الصورة القطبية لدائرة مركزها \\ltr{(0,0)} ونصف قطرها \\ltr{4}؟","56142-%D9%85%D8%A7-%D8%A7%D9%84%D8%B5%D9%88%D8%B1%D8%A9-%D8%A7%D9%84%D9%82%D8%B7%D8%A8%D9%8A%D8%A9-%D9%84%D8%AF%D8%A7%D8%A6%D8%B1%D8%A9-%D9%85%D8%B1%D9%83%D8%B2%D9%87%D8%A7-%D9%88%D9%86%D8%B5%D9%81-%D9%82%D8%B7%D8%B1%D9%87%D8%A7","ما الصورة القطبية لدائرة مركزها (0,0) ونصف قطرها 4؟ A)r = 4 B)r = 5 C)r = 6 D)r = 7 ",[287,290,293,296],{"_8":288,"_35":289},216711,"\\ltr{r = 4}",{"_8":291,"_35":292},216712,"\\ltr{r = 5}",{"_8":294,"_35":295},216713,"\\ltr{r = 6}",{"_8":297,"_35":298},216714,"\\ltr{r = 7}",[],"ما الصورة القطبية لدائرة مركزها $\"\"/$ ونصف قطرها $\"\"/$ ؟","detailedAnswer",[303,308,310,312],{"_8":54,"_35":55,"_304":27,"_305":306,"_307":-5},"is_correct","question_option_details",[],"has_access",{"_8":59,"_35":60,"_304":19,"_305":309,"_307":-5},[],{"_8":63,"_35":64,"_304":27,"_305":311,"_307":-5},[],{"_8":67,"_35":68,"_304":27,"_305":313,"_307":-5},[],"imagesURLs",[],"isMobile","questionId","streamId",1,"routes/_visitor","actionData","errors"]

أكتب العدد المركب بالصورة القطبية

أكتب العدد المركب $\ltr{2 + 2i \sqrt{3}}$ بالصورة القطبية