[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267808-105":59,"doc-detail-267808-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","unit-03-polynomial-investigations-complex-number-system-common-core-standards","Unit 03 - Polynomial Investigations - Complex Number System - Common Core Standards","","Common Core Standards define learning objectives for the Complex Number System within a Polynomial Investigations unit. Students learn the imaginary unit i and represent complex numbers in the form a + bi, perform arithmetic using i² = -1 and properties, and use conjugates to determine moduli and quotients. The unit also emphasizes solving quadratic equations with real coefficients that yield complex solutions, analyzing root nature through the discriminant, and connecting complex zeros to polynomial identities and later functions. Mathematical Practice and social-emotional standards support reasoning, modeling, and precision.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/unit-03-polynomial-investigations-complex-number-system-common-core-standards/267808/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/unit-03-polynomial-investigations-complex-number-system-common-core-standards/267808.png","ImageObject",300,407,{"name":92,"@type":93},"WPS_1786070896","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What form do students use to represent complex numbers in this unit?","Question",{"text":113,"@type":114},"Complex numbers are represented as a + bi, where a and b are real numbers, and i is the imaginary unit with i² = -1. Students also rewrite complex expressions into a + bi form.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do students use conjugates in complex number work?",{"text":118,"@type":114},"Students identify the conjugate of a complex number and multiply a complex number by its conjugate. Conjugates are used to determine moduli and quotients and to rewrite division expressions into a + bi form.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the unit connect complex numbers to solving quadratic equations?",{"text":122,"@type":114},"Students solve quadratic equations with real coefficients that have complex solutions. They analyze the nature of roots using the discriminant and apply knowledge of complex solutions and conjugates to polynomial-related contexts.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},267808,1789425095,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":24},549768072016,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Common Core Standards  \nMA.9-12. HSN-CN-The Complex Number System  \nMA.9-12. HSN-CN.A-Perform arithmetic operations with complex numbers.  \nMA.9-12. HSN-CN.1 – Know there is an imgainary number i such that i² = –1, and every complex number has the form a + bi with a and b real.  \nMA.9-12. HSN-CN.2-Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.  \nMA.9-12. HSN-CN.3-Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.  \nMA.9-12. HSN-CN. C-Use complex numbers in polynomial identities and equations.  \nMA.9-12. HSN-CN.7 – Solve quadratic equations with real coefficients that have complex solutions.  \nMathematical Practice Standards  \n X  MP1: Make sense of problems and persevere in solving them.  \n  MP2: Reason abstractly and quantitatively.  \n X  MP3: Construct viable arguments and critique the reasoning of others.  \n X  MP4: Model with mathematics.  \n X  MP5: Use appropriate tools strategically.  \n X  MP6: Attend to precision.  \n X  MP7: Look for and make use of structure.  \n  MP8: Look for and express regularity in repeated reasoning.  \nSocial-Emotional Standards  \n☒ 1A Identify and manage one’s emotions and behavior.  \n☒ 1B Recognize personal qualities and external supports.  \n☒ 1C Demonstrate skills related to achieving personal and academic goals.  \n☒ 2A Recognize the feelings and perspectives of others.  \n☐ 2B Recognize individual and group similarities and differences.  \n☒ 2C Use communication and social skills to interact effectively with others.  \n☐ 2D Demonstrate an ability to prevent, manage, and resolve interpersonal conflicts in constructive ways.☐ 3A Consider ethical, safety, and societal factors in making decisions.  \n☒ 3B Apply decision-making skills to deal responsibly with daily academic and social situations.  \n☐ 3C Contribute to the well-being of one’s school and community.  \nRationale  \n􀂃 Complex number addition, subtraction, multiplication, and division are on both ACT and SAT.  \n􀂃 Complex numbers as zeros of a polynomial function will be addressed in a subsequent unit.  \n􀂃 Complex Number addition/subtraction will be used in solving quadratic equations, as well as zeros of a polynomial function.  \n􀂃 The product of two complex numbers is an ACT/SAT topic.  \n􀂃 An understanding of complex solutions and complex conjugates is essential in understanding the zeros of a polynomial  \n􀂃 Ultimately, knowledge of the nature of roots of a quadratic equation will be essential knowledge required for success in Unit 4 – Polynomial Investigations – Functions.  \n􀂃 Being able to solve a quadratic equation in the most efficient manner is an essential skill to being able to complete the non-calculator portion of the PSAT and SAT exams.  \nPrevious Knowledge Required  \n Students have extensive experience combining like terms from Algebra 1 and Geometry.  \n Students have extensive experience in using the area model for multiplication of binomials from Algebra 1.  \n Students have extensive experience in the concept of ‘double distributive’ from Algebra 1.  \n Students have extensive experience in solving quadratic equations in a variety of ways (factoring, reversing operations, completing the square, and quadratic formula) .  \n Students have experience determining the nature of roots of a quadratic equation from Algebra 1.  \nObjective(s)  \n Understand that i 􀀠 􀀐1 is the imaginary number, cyclic exponentially with a cycle of 4.  \n Understand that a complex number is a number of the form a + bi, a and b are non-zero real number.  \n Add and subtract complex numbers.  \n Rewrite complex expressions in a + bi form.  \n Identify a number as real, imaginary, or complex.  \n Multiply complex numbers.  \n Identify the conjugate of a complex number, and multiply a complex number by its conjugate.  \n Rewrite a complex number division expression in the form a + bi.  \n Analyze quadratic equations using the discrimin","cbCaitjDXTtEYOdT","https://ap.wps.com/l/cbCaitjDXTtEYOdT","pdf",265393,"English","# Common Core Standards\n## MA.9-12 HSN-CN: Complex Number System\n## Mathematical Practice Standards\n## Social-Emotional Standards\n## Rationale\n## Previous Knowledge Required\n## Objective(s)\n## New Vocabulary","[{\"question\":\"What form do students use to represent complex numbers in this unit?\",\"answer\":\"Complex numbers are represented as a + bi, where a and b are real numbers, and i is the imaginary unit with i² = -1. Students also rewrite complex expressions into a + bi form.\"},{\"question\":\"How do students use conjugates in complex number work?\",\"answer\":\"Students identify the conjugate of a complex number and multiply a complex number by its conjugate. Conjugates are used to determine moduli and quotients and to rewrite division expressions into a + bi form.\"},{\"question\":\"How does the unit connect complex numbers to solving quadratic equations?\",\"answer\":\"Students solve quadratic equations with real coefficients that have complex solutions. They analyze the nature of roots using the discriminant and apply knowledge of complex solutions and conjugates to polynomial-related contexts.\"}]","Unit 03 - Polynomial Investigations - Complex Number System - Common Core Standards | PDF"]