// Numbas version: exam_results_page_options
{"name": "Determina el modulo y el conjugado de un n\u00famero complejo", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Determina el modulo y el conjugado de un n\u00famero complejo", "tags": [], "metadata": {"description": "<p>C&aacute;lculo del m&oacute;dulo, argumento, multiplicaci&oacute;n por conjugado complejo, dados dos n&uacute;meros complejos.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Dados los n&uacute;meros complejos $ z_1 = \\var {z1} $ y $ z_2 = \\var {z2} $.</p>\n<p>Calcule las siguientes cantidades. En lo que sigue, un asterisco denota el conjugado complejo.</p>", "advice": "<h4>a) and b)</h4>\n<p>El m&oacute;dulo de un n&uacute;mero complejo $z=a+bi$ esta dado por&nbsp;</p>\n<p>\\[\\lvert z \\rvert=\\sqrt{a^2+b^2}\\]</p>\n<p>En esta parte, $z_1 = \\var{z1}$ and $z_2 = \\var{z2}$, as&iacute;</p>\n<p>\\begin{align}<br/>\\lvert z_1 \\rvert &amp;=\\sqrt{(\\var{re(z1)})^2+(\\var{im(z1)})^2} \\\\<br/>&amp;= \\var{absz1}<br/>\\end{align}</p>\n<p>y</p>\n<p>\\begin{align}<br/>\\lvert z_2 \\rvert &amp;= \\sqrt{(\\var{re(z2)})^2+(\\var{im(z2)})^2} \\\\<br/>&amp;= \\var{absz2}<br/>\\end{align}</p>\n<p>(ambos con 3 decimales).</p>\n<h4>c)</h4>\n<p>En general</p>\n<p>\\[\\lvert z_1z_2 \\rvert=\\lvert z_1 \\rvert\\lvert z_2 \\rvert\\]</p>\n<p>Asi, en esta parte,</p>\n<p>\\[ \\lvert z_1z_2 \\rvert=\\sqrt{(\\var{re(z1)})^2+(\\var{im(z1)})^2}\\sqrt{(\\var{re(z2)})^2+(\\var{im(z2)})^2}=\\var{absz1z2} \\]</p>\n<p>Considerar hasta 3 decimales.</p>\n<h4>d)</h4>\n<p>Si $z=a+bi$, then $z^\\ast=a-bi$, entonces</p>\n<p>\\[z_1^\\ast=\\var{conjz1}\\]</p>\n<h4>e)</h4>\n<p>En general, $zz^\\ast=(a+bi)(a-bi)=a^2+b^2$, asi</p>\n<p>\\[z_1z_1^\\ast=(\\var{z1})(\\var{conjz1})=(\\var{re(z1)})^2+(\\var{im(z1)})^2=\\var{z1conjz1}.\\]</p>", "rulesets": {}, "extensions": [], "variables": {"absz1": {"name": "absz1", "group": "Ungrouped variables", "definition": "precround(abs(z1),3)", "description": "", "templateType": "anything"}, "absz2": {"name": "absz2", "group": "Ungrouped variables", "definition": "precround(abs(z2),3)", "description": "", "templateType": "anything"}, "absz1z2": {"name": "absz1z2", "group": "Ungrouped variables", "definition": "precround(abs(z1*z2),3)", "description": "", "templateType": "anything"}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "random(1..9)*sign(random(-1,1))+random(1..9)*sign(random(-1,1))*i", "description": "", "templateType": "anything"}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.001", "description": "", 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