[{"data":1,"prerenderedAt":128},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Falgebra\u002Fnumeros-complejos?{}":3,"topics-with-content:algebra":105},{"course":4,"topic":12,"counts":17,"universities":22,"channels":30,"sampleQuestions":61,"sameName":104},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},2,"algebra","Álgebra","Álg.","math","i-lucide-variable",1,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},208,"numeros-complejos","Números complejos",7,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},5,83,72,1081,[23,27],{"universityId":11,"questions":24,"years":25},3,[26],2026,{"universityId":5,"questions":5,"years":28},[26,29],2022,[31,34,37,40,42,45,48,50,52,55,57,59],{"name":32,"classes":33},"Alberto Cruz",17,{"name":35,"classes":36},"Academia ipluton",13,{"name":38,"classes":39},"Academia Internet",10,{"name":41,"classes":39},"META VILLARREAL",{"name":43,"classes":44},"Academia Grupo Ciencias",8,{"name":46,"classes":47},"Academias Aduni y César Vallejo",6,{"name":49,"classes":47},"Ciclo Uni-San Marcos",{"name":51,"classes":18},"CEPRE UNMSM",{"name":53,"classes":54},"Salón Sapiens",4,{"name":56,"classes":5},"Trilce Multimedia",{"name":58,"classes":11},"Academia_Pitagoras",{"name":60,"classes":11},"Pamer Corporación Educativa",[62,87],{"id":63,"courseId":5,"topicId":13,"pastExamId":64,"stem":65,"options":66,"correctKey":68,"explanation":82,"difficulty":5,"status":83,"source":84,"stats":85},1818,201,"¿Cuál es la relación entre los números reales $x$ e $y$, de tal manera que el número complejo\n$$z=\\frac{3x-4i}{5+yi}$$\nsea un número imaginario puro?",[67,70,73,76,79],{"key":68,"text":69},"A","$y=\\dfrac{15}{4}x$",{"key":71,"text":72},"B","$y=4x$",{"key":74,"text":75},"C","$y=\\dfrac{15}{2}x$",{"key":77,"text":78},"D","$y=x$",{"key":80,"text":81},"E","$y=-5x$","","published","UNI 2026-2 · Matemática",{"attempts":86,"accuracy":86},0,{"id":88,"courseId":5,"topicId":13,"pastExamId":89,"stem":90,"options":91,"correctKey":77,"explanation":82,"difficulty":5,"status":83,"source":102,"stats":103},5505,255,"Dados los números complejos $z_{1}=3+2i$ y $z_{2}=4+i$, determine el valor de verdad (V o F) de las siguientes proposiciones:\nI. El producto de ambos es $z_{1}\\cdot z_{2}=10+11i$\nII. El módulo de la diferencia de ellos es $\\|z_{2}-z_{1}\\|=\\|-1-i\\|=\\sqrt{2}$\nIII. La suma de sus conjugados es $\\overline{z_{1}}+\\overline{z_{2}}=-7-3i$\nIV. El cociente de ambos es $\\dfrac{z_{1}}{z_{2}}=\\dfrac{3}{4}+2i$",[92,94,96,98,100],{"key":68,"text":93},"FVFF",{"key":71,"text":95},"VFVF",{"key":74,"text":97},"FFVV",{"key":77,"text":99},"VVFF",{"key":80,"text":101},"VVVF","UNMSM 2026-I · Área A · Ciencias de la Salud",{"attempts":86,"accuracy":86},[],[64,106,107,108,109,110,111,13,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127],202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,223,225,226,1791501526889]