[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-267806-105":3,"doc-detail-267806-en":81,"detail-sidebar-cat-0-en-105":96},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","imaginary-numbers-worksheet","Imaginary Numbers Worksheet","","This document is an imaginary numbers worksheet for SAT preparation. It includes problems on identifying real and imaginary parts of complex numbers, finding conjugates, evaluating powers of i, writing expressions as complex numbers in standard form, finding absolute values, and solving quadratic equations involving complex numbers. The worksheet also provides answers to all problems. The content is designed to test and reinforce understanding of fundamental concepts in complex number arithmetic and algebra, crucial for standardized tests like the SAT. It covers operations such as addition, subtraction, multiplication, division (implied through standard form), and solving equations, essential for building a strong foundation in pre-calculus mathematics.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/imaginary-numbers-worksheet/267806/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/imaginary-numbers-worksheet/267806.png","ImageObject",300,407,{"name":42,"@type":43},"Connor ","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",17,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the difference between a real and an imaginary number in a complex number?","Question",{"text":63,"@type":64},"In a complex number of the form a + bi, 'a' is the real number part and 'bi' is the imaginary number part, where 'i' is the imaginary unit (√-1).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find the conjugate of a complex number?",{"text":68,"@type":64},"To find the conjugate of a complex number (a + bi), you change the sign of the imaginary part, resulting in (a - bi). For example, the conjugate of -2 + 4i is -2 - 4i.",{"name":70,"@type":61,"acceptedAnswer":71},"How are powers of 'i' evaluated?",{"text":72,"@type":64},"Powers of 'i' follow a cycle: i¹ = i, i² = -1, i³ = -i, and i⁴ = 1. To evaluate higher powers, you can divide the exponent by 4 and use the remainder to find the equivalent power within this cycle. For instance, i⁶ = i² = -1.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},267806,1789425089,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":91,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":92,"faqs":93,"seo_title":94,"seo_description":12,"update_tm":80,"read_time":95},687207022233,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","SATPREP  \n# Imaginary Numbers Worksheet\n\n1.For the complex number-10+4i,identify the real number and the imaginary number.  \n2.Write the conjugate of each.Then plot all eight complex numbers in the same complex plane.  \nA)-2+4iB)7iC)5D)3-2i  \nb)i¹1  \na)i⁶  \nc)i²4  \n3.Evaluate.  \n4.Write the expression as a complex number in standard form.  \nb)-i+(7-5i)-3(2-3i)a)(5+2i)+(3-2i)c)(-2+4i)+(3-9i)  \nd)(-2+4i)-(3+9i)e)(5-2i)-2(3+i)f)3i(6-5i)  \ng)i(2+i)h)(2+3i)(1-4i)i)(-3+7i)(1-2i)  \nj)(3-2i)²  \nk)(2i)(1-4i)(1+i)  \n5.Write the expression as a complex number in standard form.  \nb  \na  \nd)  \ne)  \n6.Find the absolute value of the complex number.  \nd)-2+i  \na)-2+5i  \nb)4-5i  \ne)-5i  \nc)1-5i  \n7.Solve each equation.  \nc)x²+4x=-20 d)x²=8x-35a)4x²+20=0b)4x²+5=-7  \nf)3(x+4)²=-27 g)8r²+4r+5=0 h)6p²-8p=-3e)x²+4x=-29  \n# Answers\n\n1.Real number:-10;Imaginary number:4i  \n2.A)-2-4iB)-7iC)5D)3+2i  \n3.a)-1b)-ic)1  \n4.a)8b)1+3ic)1-5id)-5-5ie)-1-4i f)15+18ig)-1+2i  \nk)(2i)(1-3i-4i²)=(2i)(5-3i)=(10i-6i²)=6+10i  \nh)14-5i i)11+13ij)13-12i5 a)  \nq  \n6.a)√29b)√41c)√26d)√5  \ne)5  \n7.a)±i√5b)±i√3  \nc)-2±4id)4±i√19 e)-2±5if)-4±3i  \ng  \n句","cbCaif8VbzdtFKgC","https://ap.wps.com/l/cbCaif8VbzdtFKgC","pdf",1246272,"English","# Imaginary Numbers Worksheet\n1.Real and Imaginary Numbers\n2.Conjugates and Plotting\n3.Evaluating Powers of i\n4.Standard Form Expressions\n5.Standard Form Expressions\n6.Absolute Value\n7.Solving Equations\n# Answers","[{\"question\":\"What is the difference between a real and an imaginary number in a complex number?\",\"answer\":\"In a complex number of the form a + bi, 'a' is the real number part and 'bi' is the imaginary number part, where 'i' is the imaginary unit (√-1).\"},{\"question\":\"How do you find the conjugate of a complex number?\",\"answer\":\"To find the conjugate of a complex number (a + bi), you change the sign of the imaginary part, resulting in (a - bi). For example, the conjugate of -2 + 4i is -2 - 4i.\"},{\"question\":\"How are powers of 'i' evaluated?\",\"answer\":\"Powers of 'i' follow a cycle: i¹ = i, i² = -1, i³ = -i, and i⁴ = 1. To evaluate higher powers, you can divide the exponent by 4 and use the remainder to find the equivalent power within this cycle. For instance, i⁶ = i² = -1.\"}]","Imaginary Numbers Worksheet | PDF",5,{"code":4,"msg":82,"data":97},[98,102,106,109,113,118,123,128,133,136,140],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":107,"slug":108},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},"Comic",60,"comic",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},6,"Technology",50,"technology",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},7,"Healthcare",40,"healthcare",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":126,"slug":127},8,"Research & Report",30,"research-report",{"id":129,"doc_module":4,"doc_module_name":25,"category_name":130,"show_sort_weight":131,"slug":132},9,"Religion & Spirituality",20,"religion-spirituality",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":134,"show_sort_weight":131,"slug":135},"World Cup","world-cup",{"id":137,"doc_module":4,"doc_module_name":25,"category_name":138,"show_sort_weight":137,"slug":139},10,"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":25,"category_name":142,"show_sort_weight":95,"slug":143},19,"General","general"]