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$z_1+z_2=$
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "name": "Complex number arithmetic", "variables": {"z1plusz2": {"name": "z1plusz2", "description": "", "group": "Ungrouped variables", "definition": "z1+z2", "templateType": "anything"}, "z3": {"name": "z3", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "templateType": "anything"}, "modz4sq": {"name": "modz4sq", "description": "", "group": "Ungrouped variables", "definition": "z4*z4bar", "templateType": "anything"}, "z3z4bar": {"name": "z3z4bar", "description": "", "group": "Ungrouped variables", "definition": "z3*z4bar", "templateType": "anything"}, "z4bar": {"name": "z4bar", "description": "", "group": "Ungrouped variables", "definition": "conj(z4)", "templateType": "anything"}, "z4": {"name": "z4", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "templateType": "anything"}, "z1z3": {"name": "z1z3", "description": "", "group": "Ungrouped variables", "definition": "z1*z3", "templateType": "anything"}, "re_z3onz4": {"name": "re_z3onz4", "description": "", "group": "Ungrouped variables", "definition": "re(z3/z4)", "templateType": "anything"}, "z1": {"name": "z1", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "templateType": "anything"}, "z2": {"name": "z2", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10)+random(-10..10)i", "templateType": "anything"}, "z1minusz2": {"name": "z1minusz2", "description": "", "group": "Ungrouped variables", "definition": "z1-z2", "templateType": "anything"}, "im_z3onz4": {"name": "im_z3onz4", "description": "", "group": "Ungrouped variables", "definition": "im(z3/z4)", "templateType": "anything"}}, "ungrouped_variables": ["z1", "z2", "z3", "z4", "z4bar", "z3z4bar", "modz4sq", "re_z3onz4", "im_z3onz4", "z1plusz2", "z1minusz2", "z1z3"], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "statement": "This question will help you to practice adding, subtracting, multiplying and dividing complex numbers in Cartesian/rectangular form. If you wish, you might like to watch this video which explains these operations and how to do problems like these.
\n\nGiven the complex numbers
\n\\[z_1=\\var{z1},\\quad z_2=\\var{z2}, \\quad z_3=\\var{z3}, \\quad z_4=\\var{z4},\\]
\ncalculate the following (write your answers in Cartesian/rectangular form).
", "functions": {}, "advice": "\\[z_1+z_2=(\\var{z1})+(\\var{z2})=\\simplify{{z1}+{z2}}\\]
\n\\[z_1-z_2=(\\var{z1})-(\\var{z2})=\\simplify{{z1}-{z2}}\\]
\n\\[z_1z_3=(\\var{z1})(\\var{z3})=\\var{z1z3}\\]
\n\\[\\frac{z_3}{z_4}=\\frac{\\var{z3}}{\\var{z4}}=\\frac{(\\var{z3})(\\var{z4bar})}{(\\var{z4})(\\var{z4bar})}=\\simplify{{z3z4bar}/{modz4sq}}\\approx \\var{re_z3onz4}+\\var{im_z3onz4}\\]
", "preamble": {"js": "", "css": ""}, "rulesets": {}, "type": "question", "contributors": [{"name": "Dann Mallet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/800/"}]}]}], "contributors": [{"name": "Dann Mallet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/800/"}]}