// Numbas version: exam_results_page_options {"name": "Complex Numbers; Basics 02", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Complex Numbers; Basics 02", "tags": [], "metadata": {"description": "Identify Real and Imaginary parts of a complex number", "licence": "All rights reserved"}, "statement": "
where $a$ and $b$ are real numbers (including $0$) and $i$ is an imaginary number, $i=\\sqrt{-1}$.
\nGenerally, $a$ is called the real part of $z$, or $\\mathbb{Re}(z)$ and $b$ is called the imaginary part of $z$ or $\\mathbb{Im}(z)$
", "advice": "The only things that we need to remember are:
\n$\\large z_1=\\var{r1}+ \\var{i1}i$
\n$\\mathbb{Re}(z_1)=\\var{r1}$ $\\mathbb{Im}(z_1)=\\var{i1}$
\n\n
$\\large z_2=\\var{r2}+ \\var{i2}i$
\n$\\mathbb{Re}(z_2)=\\var{r2}$ $\\mathbb{Im}(z_2)=\\var{i2}$
\n\n
$\\large z_3=\\var{r3}+ \\var{i3}i$
\n$\\mathbb{Re}(z_3)=\\var{r3}$ $\\mathbb{Im}(z_3)=\\var{i3}$
\n\n
$\\large z_4=\\simplify{{r4}+ {i4}i}$
\n$\\mathbb{Re}(z_4)=\\var{r4}$ $\\mathbb{Im}(z_4)=\\var{i4}$
\n\n
$\\large z_5=\\simplify{{r5}+ {i5}i}$
\n$\\mathbb{Re}(z_5)=\\var{r5}$ $\\mathbb{Im}(z_5)=\\var{i5}$
", "rulesets": {}, "extensions": [], "variables": {"r1": {"name": "r1", "group": "CN1", "definition": "random(2..25)", "description": "", "templateType": "anything"}, "i1": {"name": "i1", "group": "CN1", "definition": "random(2..25 except r1)", "description": "", "templateType": "anything"}, "r2": {"name": "r2", "group": "CN2", "definition": "random(2..25 except r1)", "description": "", "templateType": "anything"}, "i2": {"name": "i2", "group": "CN2", "definition": "random(2..25 except r1 except r2)", "description": "", "templateType": "anything"}, "r3": {"name": "r3", "group": "CN3", "definition": "random(-25..25 except 0 except r1 except r2)", "description": "", "templateType": "anything"}, "i3": {"name": "i3", "group": "CN3", "definition": "random(2..25 except r3 except r1 except r2)", "description": "", "templateType": "anything"}, "r4": {"name": "r4", "group": "CN4", "definition": "random(-10..10)", "description": "", "templateType": "anything"}, "i4": {"name": "i4", "group": "CN4", "definition": "random(-10..10 except 0 except r4)", "description": "", "templateType": "anything"}, "r5": {"name": "r5", "group": "CN5", "definition": "random(-10..10 except r4)", "description": "", "templateType": "anything"}, "i5": {"name": "i5", "group": "CN5", "definition": "random(-10..10 except r5)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "CN1", "variables": ["r1", "i1"]}, {"name": "CN2", "variables": ["r2", "i2"]}, {"name": "CN3", "variables": ["r3", "i3"]}, {"name": "CN4", "variables": ["r4", "i4"]}, {"name": "CN5", "variables": ["r5", "i5"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "\n
$\\large z_1=\\var{r1}+ \\var{i1}i$
\n$\\mathbb{Re}(z_1)=$ [[0]] $\\mathbb{Im}(z_1)=$ [[1]]
\n\n
$\\large z_2=\\var{r2}+ \\var{i2}i$
\n$\\mathbb{Re}(z_2)=$ [[2]] $\\mathbb{Im}(z_2)=$ [[3]]
\n\n
$\\large z_3=\\var{r3}+ \\var{i3}i$
\n$\\mathbb{Re}(z_3)=$ [[4]] $\\mathbb{Im}(z_3)=$ [[5]]
\n\n
$\\large z_4=\\simplify{{r4}+ {i4}i}$
\n$\\mathbb{Re}(z_4)=$ [[6]] $\\mathbb{Im}(z_4)=$ [[7]]
\n\n
$\\large z_5=\\simplify{{r5}+ {i5}i}$
\n$\\mathbb{Re}(z_5)=$ [[8]] $\\mathbb{Im}(z_5)=$ [[9]]
\n", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{r1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{i1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{r2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{i2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{r3}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{i3}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{r4}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{i4}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{r5}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{i5}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}