[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522719-105":59,"doc-detail-522719-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","operations-with-complex-numbers-worksheet-simplify","Operations with Complex Numbers - Worksheet - Simplify","","Algebra worksheet focused on simplifying expressions involving complex numbers. Students practice reducing sums, differences, products, and powers of terms containing the imaginary unit i, including combinations like (a+bi)(c+di) and (1-7i)^2. The set includes multiple numbered problems that require distributing, combining like terms, and using i^2 = -1. A critical-thinking section asks students to compare structurally similar expressions with i versus x and determine whether they differ.",{"@graph":69,"@context":122},[70,84,105],{"@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/operations-with-complex-numbers-worksheet-simplify/522719/",{"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/operations-with-complex-numbers-worksheet-simplify/522719.png","ImageObject",300,407,{"name":92,"@type":93},"Jacob","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kind of math skills does the worksheet emphasize?","Question",{"text":112,"@type":113},"It emphasizes simplifying expressions with complex numbers, including distributing products, combining like terms, and handling powers of expressions that involve the imaginary unit i.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What role does i^2 = -1 play in these problems?",{"text":117,"@type":113},"It provides the key substitution used to simplify powers and products involving i, turning expressions with i^2 into real numbers.",{"name":119,"@type":110,"acceptedAnswer":120},"What do the critical thinking questions ask students to do?",{"text":121,"@type":113},"They compare paired problems to decide whether expressions simplify differently when using x versus using i, and they judge whether there is any real structural difference.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522719,1791519005,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Algebra 2 Name   \nOperations with Complex Numbers Date  Period   \nSimplify.  \n1) i + 6i 2) 3 + 4 + 6i  \n3) 3i + i 4) −8i − 7i  \n5) −1 − 8i − 4 − i 6) 7 + i + 4 + 4  \n7) −3 + 6i − (−5 − 3i) − 8i 8) 3 + 3i + 8 − 2i − 7  \n9) 4i(−2 − 8i) 10) 5i ⋅ −i  \n11) 5i ⋅ i ⋅ −2i 12) −4i ⋅ 5i  \n13) (−2 − i)(4 + i) 14) (7 − 6i)(−8 + 3i)  \n15) 7i ⋅ 3i(−8 − 6i) 16) (4 − 5i)(4 + i)  \n17) (2 − 4i)(−6 + 4i) 18) (−3 + 2i)(−6 − 8i)  \n19) (8 − 6i)(−4 − 4i) 20) ( 1 − 7i)2  \n21) 6(−7 + 6i)(−4 + 2i) 22) (−2 − 2i)(−4 − 3i)(7 + 8i)  \n23) 5i + 7i ⋅ i 24) (6i) 3  \n25) 6i ⋅ −4i + 8 26) −6(4 − 6i)  \n27) (8 − 3i)2 28) 3 + 7i − 3i − 4  \n29) −3i ⋅ 6i − 3(−7 + 6i) 30) −6i(8 − 6i)(−8 − 8i)  \nCritical thinking questions:  \n31) How are the following problems different?  \nSimplify: (2 + x)(3 − 2x)  \nSimplify: (2 + i)(3 − 2i)  \n32) How are the following problems different?  \nSimplify: 2 + x − (3 − 2x)  \nSimplify: 2 + i − (3 − 2i)  \nKuta Software-Infinite Algebra 2 Name   \nOperations with Complex Numbers Date  Period   \nSimplify.  \n1) i + 6i  \n7i  \n2) 3 + 4 + 6i  \n7 + 6i  \n3) 3i + i 4) −8i − 7i  \n4i −15i  \n5) −1 − 8i − 4 − i 6) 7 + i + 4 + 4  \n−5 − 9i 15 + i  \n7) −3 + 6i − (−5 − 3i) − 8i 8) 3 + 3i + 8 − 2i − 7  \n2 + i 4 + i  \n9) 4i(−2 − 8i) 10) 5i ⋅ −i  \n32 − 8i 5  \n11) 5i ⋅ i ⋅ −2i 12) −4i ⋅ 5i  \n10i 20  \n13) (−2 − i)(4 + i) 14) (7 − 6i)(−8 + 3i)  \n−7 − 6i −38 + 69i  \n15) 7i ⋅ 3i(−8 − 6i) 16) (4 − 5i)(4 + i)  \n168 + 126i 21 − 16i  \n17) (2 − 4i)(−6 + 4i)  \n4 + 32i  \n19) (8 − 6i)(−4 − 4i)  \n−56 − 8i  \n21) 6(−7 + 6i)(−4 + 2i)  \n96 − 228i  \n23) 5i + 7i ⋅ i  \n−7 + 5i  \n25) 6i ⋅ −4i + 8 32  \n27) (8 − 3i)2  \n55 − 48i  \n29) −3i ⋅ 6i − 3(−7 + 6i)  \n39 − 18i  \n18) (−3 + 2i)(−6 − 8i)  \n34 + 12i  \n20) ( 1 − 7i)2  \n−48 − 14i  \n22) (−2 − 2i)(−4 − 3i)(7 + 8i)  \n−98 + 114i  \n24) (6i) 3  \n−216i  \n26) −6(4 − 6i)  \n−24 + 36i  \n28) 3 + 7i − 3i − 4  \n−1 + 4i  \n30) −6i(8 − 6i)(−8 − 8i)  \n−96 + 672i  \nCritical thinking questions:  \n31) How are the following problems different?  \nSimplify: (2 + x)(3 − 2x)  \nSimplify: (2 + i)(3 − 2i)  \ni² = −1 so it leads to a few more steps  \n32) How are the following problems different?  \nSimplify: 2 + x − (3 − 2x)  \nSimplify: 2 + i − (3 − 2i)  \nThere is no difference.  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCainwuwBGTJ1HI","https://ap.wps.com/l/cbCainwuwBGTJ1HI","pdf",33302,"English","# Simplify Complex Number Expressions\n## Practice Problems 1-30\n## Critical Thinking Questions 31-32","[{\"question\":\"What kind of math skills does the worksheet emphasize?\",\"answer\":\"It emphasizes simplifying expressions with complex numbers, including distributing products, combining like terms, and handling powers of expressions that involve the imaginary unit i.\"},{\"question\":\"What role does i^2 = -1 play in these problems?\",\"answer\":\"It provides the key substitution used to simplify powers and products involving i, turning expressions with i^2 into real numbers.\"},{\"question\":\"What do the critical thinking questions ask students to do?\",\"answer\":\"They compare paired problems to decide whether expressions simplify differently when using x versus using i, and they judge whether there is any real structural difference.\"}]","Operations with Complex Numbers - Worksheet - Simplify | PDF",1791426094]