// Numbas version: finer_feedback_settings
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Four parts.</p>\n<p>Original: https://numbas.mathcentre.ac.uk/question/11785/arithmetics-of-complex-numbers-ii/ by Newcastle University Mathematics and Statistics</p>\n<p>Translated to German.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Schreiben Sie die folgenden komplexen Zahlen in der Form $a+bi\\;$ f&uuml;r reelle Zahlen $a$ und $b$.</p>\n<p>Geben Sie alle Zahlen als Bruchzahlen oder als ganze Zahlen an.</p>", "advice": "<p><strong>a)</strong></p>\n<p>Die L&ouml;sung ist</p>\n<p><br/>$\\simplify[std]{{e6*i}}(\\simplify[std]{{a}})=\\simplify[std]{{a*e6*i}}$</p>\n<p><br/><strong>b)</strong></p>\n<p>$\\simplify[std]{{a}*{z4}={a*z4}}$</p>\n<p><br/><strong>c)</strong></p>\n<p>\\[ \\begin{eqnarray*} \\simplify[std,!otherNumbers]{{a}*({a3} + {b3} * i + {c3} * i ^ 2 + {d3} * i ^ 3)}&amp;=&amp;\\simplify[std]{{a}*{a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3}}\\\\ &amp;=&amp;\\simplify[std]{{a*(a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3)}} \\end{eqnarray*} \\]</p>\n<p><strong>d)</strong></p>\n<p>Rechnen Sie in mehreren Schritten:</p>\n<p>\\[ \\begin{eqnarray*} (\\var{a})(\\var{z1})(\\var{z3})&amp;=&amp;((\\var{a})(\\var{z1}))(\\var{z3})\\\\ &amp;=&amp;(\\var{a*(z1)})(\\var{z3})\\\\ &amp;=&amp;\\var{a*(z1)*(z3)} \\end{eqnarray*} \\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "s1*random(1..9)+s2*random(1..9)*i", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "s4": {"name": "s4", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "s3*random(1..9)+f6*i", "description": "", "templateType": "anything"}, "d3": {"name": "d3", "group": "Ungrouped 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"s6*random(1..9)", "description": "", "templateType": "anything"}, "d6": {"name": "d6", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything"}, "c3": {"name": "c3", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything"}, "s3": {"name": "s3", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "s2*random(1..9)+d6*i", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "s6": {"name": "s6", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "f6", "s3", "s2", "s1", "d3", "s6", "s5", "s4", 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