{"@context":"https://schema.org/","@type":"Quiz","name":"

Simplify the expression $(1+i)^{8}$

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"NET"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"NET","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/simplify-the-expression-1-i-8"}],"about":{"@type":"Thing","name":"NET, NUST Entry Test, Mathematics, Number System, Quiz"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["NET","NUST Entry Test","Mathematics","Number System","Quiz"],"name":"

Simplify the expression $(1+i)^{8}$

","comment":{"@type":"Comment","text":"

$(1+i)^{8}$

$=[(1+i)^{2}]^{4}$

$=(1+i^{2}+2i)^{4}$ $\\because (a+b)^{2}=a^{2}+b^{2}+2ab$

$=(1-1+2i)^{4}$ $\\because i^{2}=-1$

$=(2i)^{4}$

$=16i^{4}$

$=16(i^{2})^{2}$

$=16(-1)^{2}$

$=16$

"},"encodingFormat":"text/markdown","text":"

Simplify the expression $(1+i)^{8}$

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$-16$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$32$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$-32$

"}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$16$

","comment":{"@type":"Comment","text":"

$(1+i)^{8}$

$=[(1+i)^{2}]^{4}$

$=(1+i^{2}+2i)^{4}$ $\\because (a+b)^{2}=a^{2}+b^{2}+2ab$

$=(1-1+2i)^{4}$ $\\because i^{2}=-1$

$=(2i)^{4}$

$=16i^{4}$

$=16(i^{2})^{2}$

$=16(-1)^{2}$

$=16$

"},"answerExplanation":{"@type":"Comment","text":"

$(1+i)^{8}$

$=[(1+i)^{2}]^{4}$

$=(1+i^{2}+2i)^{4}$ $\\because (a+b)^{2}=a^{2}+b^{2}+2ab$

$=(1-1+2i)^{4}$ $\\because i^{2}=-1$

$=(2i)^{4}$

$=16i^{4}$

$=16(i^{2})^{2}$

$=16(-1)^{2}$

$=16$

"}}},"url":"https://classnotes.xyz/mcqs/simplify-the-expression-1-i-8"}