// Numbas version: exam_results_page_options
{"name": "Complex Numbers; Addition & Subtraction 01", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Complex Numbers; Addition & Subtraction 01", "tags": [], "metadata": {"description": "Addition and subtraction of complex numbers", "licence": "All rights reserved"}, "statement": "<h4>Let $z$ and $w$ be any two complex numbers</h4>\n<h4 style=\"text-align: center;\">$&nbsp; &nbsp;z=a+bi&nbsp; &nbsp;$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; and&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;$&nbsp; &nbsp;w=c+di&nbsp; &nbsp;$&nbsp;</h4>\n<h4 style=\"text-align: left;\">Then&nbsp;</h4>\n<h4 style=\"text-align: center;\">$z + w = (a + c) + (b + d)i$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; and&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $z &minus; w = (a &minus; c) + (b &minus; d)i$</h4>", "advice": "<h4>We are asked to evaluate the following additions and subtractions in complex numbers.</h4>\n<p>The technique is very straight forward - add (or subtract) the real parts, then add (or subtract) the imaginary parts.</p>\n<h4>Given:</h4>\n<p>$\\large z_1=\\var{z1}$&nbsp; &nbsp; &nbsp;and&nbsp; &nbsp; &nbsp;&nbsp;$\\large z_2=\\var{z2}$</p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_1+z_2=(\\var{z1})+(\\var{z2})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_1+z_2=(\\var{r1}+\\var{r2})+(\\var{i1}+\\var{i2})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_1+z_2=\\simplify{{z1}+{z2}}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_1-z_2=(\\var{z1})-(\\var{z2})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_1-z_2=(\\var{r1}-\\var{r2})+(\\var{i1}--\\var{i2})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_1-z_2=\\simplify{{z1}-{cc2}}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_2-z_1=(\\var{z2})-(\\var{z1})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_2-z_1=(\\var{r2}-\\var{r1})+(\\var{i2}-\\var{i1})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_2-z_1=\\simplify{{z2}-{z1}}$</p>\n<hr/>\n<h4>Given:</h4>\n<p>$\\large z_3=\\var{z3}$&nbsp; &nbsp; &nbsp;and&nbsp; &nbsp; &nbsp;&nbsp;$\\large z_4=\\var{z4}$</p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_3+z_4=(\\var{z3})+(\\var{z4})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_3+z_4=(\\var{r3}+\\var{r4})+(\\var{i3}+\\var{i4})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_3+z_4=\\simplify{{z3}+{z4}}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_3-z_4=(\\var{z3})-(\\var{z4})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_3-z_4=(\\var{r3}-\\var{r4})+(\\var{i3}-\\var{i4})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_3-z_4=\\simplify{{z3}-{z4}}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_4-z_3=(\\var{z4})-(\\var{z3})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_4-z_3=(\\var{r4}-\\var{r3})+(\\var{i4}-\\var{i3})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_4-z_3=\\simplify{{z4}-{z3}}$</p>\n<hr/>\n<h4>Given:</h4>\n<p>$\\large z_5=\\var{z5}$&nbsp; &nbsp; &nbsp;and&nbsp; &nbsp; &nbsp;&nbsp;$\\large z_6=\\var{cc1}$</p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_5+z_6=(\\var{z5})+(\\var{cc1})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6=(\\var{r5}+\\var{r1})+(\\var{i5}+-\\var{i1})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6=\\simplify{{z5}+{cc1}}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5-z_6=(\\var{z5})-(\\var{cc1})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5-z_6=(\\var{r5}-\\var{r1})+(\\var{i5}- -\\var{i1})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5-z_6=\\simplify{{z5}-{cc1}}$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_6-z_5=(\\var{cc1})-(\\var{z5})$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_6-z_5=(\\var{r1}- \\var{r5})+( -\\var{i1}-\\var{i5})i$&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_6-z_5=\\simplify{{cc1}-{z5}}$</p>\n<hr/>\n<h4>Given:</h4>\n<p>$\\large z_5=\\var{z5}$,&nbsp; &nbsp; &nbsp; $\\large z_6=\\var{cc1}$&nbsp;&nbsp; &nbsp;and&nbsp; &nbsp; &nbsp; $\\large z_7=\\var{cc2}$</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">You need to remember your BODMAS (order of operations) rules when you have more than two numbers to deal with.</p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_5+z_6+z_7=(\\var{z5})+(\\var{cc1})+(\\var{cc2})$</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6+z_7=(\\var{r5}+\\var{r1}+\\var{r2})+(\\var{i5}+-\\var{i1}+-\\var{i2})i$</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6+z_7=\\simplify{ {z5}+{cc1}+{cc2}&nbsp; &nbsp; }$</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6-z_7=(\\var{z5})+(\\var{cc1})-(\\var{cc2})$</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6-z_7=(&nbsp; \\var{r5}+\\var{r1}-\\var{r2}&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;)+(&nbsp; &nbsp; \\var{i5}+-\\var{i1}--\\var{i2}&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;)i$</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6-z_7=\\simplify{ {z5}+{cc1}-{cc2}&nbsp; &nbsp; }$</p>\n<p style=\"text-align: center;\">&nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, 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"description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "CN1", "variables": ["r1", "i1", "z1", "cc1", "rcc1"]}, {"name": "CN2", "variables": ["r2", "i2", "z2", "cc2"]}, {"name": "CN3", "variables": ["r3", "i3", "z3", "cc3"]}, {"name": "CN4", "variables": ["r4", "i4", "z4", "cc4"]}, {"name": "CN5", "variables": ["r5", "i5", "z5", "cc5"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<h4>If:</h4>\n<p>$\\large z_1=\\var{z1}$&nbsp; &nbsp; &nbsp;and&nbsp; &nbsp; &nbsp;&nbsp;$\\large z_2=\\var{z2}$</p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_1+z_2=$ [[0]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_1-z_2=$ [[1]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_2-z_1=$ [[2]]</p>\n<hr/>\n<h4>If:</h4>\n<p>$\\large z_3=\\var{z3}$ &nbsp; &nbsp;and&nbsp; &nbsp; &nbsp; $\\large z_4=\\var{z4}$</p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_3+z_4=$ [[3]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_3-z_4=$ [[4]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_4-z_3=$ [[5]]</p>\n<hr/>\n<h4>If:</h4>\n<p>$\\large z_5=\\var{z5}$,&nbsp; &nbsp; &nbsp; $\\large z_6=\\var{cc1}$&nbsp;&nbsp; &nbsp;and&nbsp; &nbsp; &nbsp; $\\large z_7=\\var{cc2}$</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"></p>\n<h4 style=\"text-align: left;\">Evaluate:</h4>\n<p style=\"text-align: center;\">$\\large z_5+z_6+z_7=$ [[6]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$\\large z_5+z_6-z_7=$ [[7]]</p>\n<p style=\"text-align: center;\"></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{z1}+{z2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], 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