[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267803-105":59,"doc-detail-267803-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","imaginary-complex-numbers-practice-questions-conjugate-fractions-practice-questions","Imaginary & Complex Numbers Practice Questions - Conjugate Fractions Practice Questions","","Imaginary and complex numbers practice questions focus on simplifying sums, evaluating products, and determining equivalent values involving i (with i ≠ −1). Tasks require adding complex numbers, solving algebraic expressions that include powers of i, and rewriting results in the a + bi form to extract real and imaginary components. A second set emphasizes conjugate fractions, including free-response transformations, coefficient identification, and solving for constants under algebraic constraints. No calculator use is required.",{"@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/imaginary-complex-numbers-practice-questions-conjugate-fractions-practice-questions/267803/",{"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/imaginary-complex-numbers-practice-questions-conjugate-fractions-practice-questions/267803.png","ImageObject",300,407,{"name":92,"@type":93},"\tWilliam","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why is a calculator not allowed for these questions?","Question",{"text":113,"@type":114},"The worksheet explicitly instructs not to use a calculator, so all answers must be obtained through algebraic manipulation of imaginary and complex expressions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you handle powers of i in these problems?",{"text":118,"@type":114},"Each question relies on simplifying expressions using the fact that i is the imaginary unit (given as i ≠ −1), so powers of i must be reduced to real and imaginary components when rewriting in a + bi form.",{"name":120,"@type":111,"acceptedAnswer":121},"What does it mean to rewrite an expression in the form a + bi?",{"text":122,"@type":114},"It means expressing the complex number so the real part is a and the imaginary part is b; then the question asks for either a or b specifically.","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},267803,1789425081,{"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":19,"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":52},5909887254083,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Imaginary & Complex Numbers Practice Questions  \nDO NOT USE A CALCULATOR ON ANY OF THE FOLLOWING QUESTIONS.  \n1. For i 􀀠 􀀐1 , what is the sum of (􀀐4 􀀎 7i) 􀀎 (􀀐3 􀀐 2i) ?  \n(A) 􀀐 7 􀀐 5i  \n(B) 􀀐 7 􀀎 5i  \n(C) 􀀐1􀀐 9i  \n(D) 7 􀀎 9i  \n2. What is the sum of the complex numbers  \n4 􀀎 3i and 5 􀀎 6i , where i 􀀠 􀀐1 ?  \n(A) 20  \n(B) 20i  \n(C) 9 􀀎 9i  \n(D) 20 􀀎18i  \n3. Which of the following complex numbers is equal to (2 􀀎11i) 􀀐 (3i2 􀀎 7) , for i 􀀠 􀀐1 ?  \n(A) 􀀐 8 􀀎11i  \n(B) 􀀐 5 􀀎 8i  \n(C) 􀀐 2 􀀎11i  \n(D) 12 􀀎11i  \n4. Which of the following complex numbers is equal to (12 􀀐 4i2 ) 􀀐 (14 􀀐 8i2 􀀎 2i) , for i 􀀠 􀀐1 ?  \n(A) 10 􀀐 2i  \n(B) 2 􀀎 2i  \n(C) 􀀐 6 􀀎 2i  \n(D) 􀀐 6 􀀐 2i  \n5. Which of the following values is equivalent to (􀀐6 􀀐 4i 􀀎 i2 ) 􀀐 2(4 􀀐 3i2 􀀐 2i) , for i 􀀠 􀀐1 ?  \n(A) 􀀐 21  \n(B) 􀀐 9  \n(C) 􀀐14 􀀐 2i  \n(D) 􀀐 21􀀐 8i  \n4 􀀐 2i 1􀀎 i  \n7. If the expression above is rewritten in the forma 􀀎 bi , where a and b are real numbers, what is the value of a ? (Note: i 􀀠 􀀐1 )  \n(A) 􀀐 4  \n(B) 􀀐1  \n(C) 1  \n(D) 4  \n6. Which of the following values is equivalent to  \n􀀐 3i2 (4i 􀀐 i2 ) 􀀐 2i2 (1􀀎 5i2 􀀎 6i) , for i 􀀠 􀀐1 ?  \n(A) 􀀐11  \n(B) 􀀐 5 􀀎 24i  \n(C) 11􀀎 24i  \n(D) 11  \n6 􀀎 2i  \n3 􀀐 4i  \n8. If the expression above is rewritten in the forma 􀀎 bi , where a and b are real numbers, what is the value of b ? (Note: i 􀀠 􀀐1 )  \n(A) 25 (B) 12 (C) 65 (D) 2  \nConjugate Fractions Practice Questions  \nDO NOT USE A CALCULATOR ON THE FOLLOWING QUESTIONS.  \n 1  􀀎 4  \n4x 􀀎 2  \n1. Which of the following is equivalent to the expression above for x 􀁺 12 ?  \n(A) 4x5􀀎~~ ~~2 (B) 4x4x~~ ~~􀀎􀀎~~ ~~92 (C) 16x4x􀀎􀀎52  \n(D) 16x4x􀀎􀀎92  \n6 􀀐  6  \n3 􀀎 ~~ ~~6  \n2. FREE RESPONSE: If the equation above is rewritten in the form a 􀀎 b6 , where a and b are constants, what is the value of a 􀀎 b ?  \n7x 􀀎 9 7  \n~~ ~~ 􀀐 ~~ ~~  \n(x 􀀎1)2 x 􀀎1  \n3. FREE RESPONSE: The expression above is equivalent to (x~~ ~~n􀀎1)2~~ ~~ where n is a positive constant and x 􀁺 􀀐1 . What is the value of n ?  \n6 􀀎 52  \n6 􀀐 22  \n4. If the equation above is rewritten in the forma 􀀎 b ~~ ~~2 , where a and b are constants, what is the value of a ?  \n(A) 1  \n(B) 1141  \n(C) 74 (D) 2  \n12x2~~ ~~􀀎ax20􀀎x4~~ ~~􀀐~~ ~~39 􀀠 􀀐3x 􀀐 8 􀀐 ~~ ~~ax7􀀎~~ ~~4  \n5. The equation above is true for all values of x 􀁺 􀀐 ~~ ~~4a , where a is a constant. What is the value of a ?  \n(A) 􀀐15  \n(B) 􀀐 4 (C) 4  \n(D) 15  \n100 􀀐 50i  \n1􀀎 3i  \n6. If the expression above is rewritten in the forma 􀀎 bi , where a and b are real numbers, what is the value of b ? (Note: i 􀀠 􀀐1 )  \n(A) 􀀐 35  \n(B) 25  \n(C) 50  \n(D) 100  \n5 􀀎 205  \n2 􀀐 ~~ ~~5  \n7. If the equation above is rewritten in the forma 􀀎 b5 , where a and b are constants, what is the value of a 􀀐 b ?  \n(A) 􀀐155  \n(B) 􀀐 65  \n(C) 65  \n(D) 155  \n20i 􀀎 32  \n2i 􀀐 2  \n8. If the expression above is rewritten in the forma 􀀎 bi , where a and b are real numbers, what is the value of a ? (Note: i 􀀠 􀀐1 )  \n(A) 􀀐13  \n(B) 􀀐 3 (C) 3  \n(D) 10","cbCaijffPmOf8iKF","https://ap.wps.com/l/cbCaijffPmOf8iKF","pdf",206099,"English","# Imaginary & Complex Numbers Practice Questions\n## Complex number sums and equivalences\n## Rewriting in a + bi form\n# Conjugate Fractions Practice Questions\n## Equivalent expressions and simplification\n## Free response for constants a and b","[{\"question\":\"Why is a calculator not allowed for these questions?\",\"answer\":\"The worksheet explicitly instructs not to use a calculator, so all answers must be obtained through algebraic manipulation of imaginary and complex expressions.\"},{\"question\":\"How do you handle powers of i in these problems?\",\"answer\":\"Each question relies on simplifying expressions using the fact that i is the imaginary unit (given as i ≠ −1), so powers of i must be reduced to real and imaginary components when rewriting in a + bi form.\"},{\"question\":\"What does it mean to rewrite an expression in the form a + bi?\",\"answer\":\"It means expressing the complex number so the real part is a and the imaginary part is b; then the question asks for either a or b specifically.\"}]","Imaginary & Complex Numbers Practice Questions - Conjugate Fractions Practice Questions | PDF"]