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$z_1+z_2=$

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$z_1-z_2=$

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$z_1z_3=$

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$\\displaystyle\\frac{z_3}{z_4}=$

", "variableReplacementStrategy": "originalfirst", "answer": "{re_z3onz4}+{im_z3onz4}i", "marks": 1, "showFeedbackIcon": true}], "name": "Complex number arithmetic", "variables": {"z4": {"definition": "random(-10..10)+random(-10..10)i", "description": "", "templateType": "anything", "name": "z4", "group": "Ungrouped variables"}, "z3": {"definition": "random(-10..10)+random(-10..10)i", "description": "", "templateType": "anything", "name": "z3", "group": "Ungrouped variables"}, "z1": {"definition": "random(-10..10)+random(-10..10)i", "description": "", "templateType": "anything", "name": "z1", "group": "Ungrouped variables"}, "z3z4bar": {"definition": "z3*z4bar", "description": "", "templateType": "anything", "name": "z3z4bar", "group": "Ungrouped variables"}, "z1plusz2": {"definition": "z1+z2", "description": "", "templateType": "anything", "name": "z1plusz2", "group": "Ungrouped variables"}, "z4bar": {"definition": "conj(z4)", "description": "", "templateType": "anything", "name": "z4bar", "group": "Ungrouped variables"}, "z1minusz2": {"definition": "z1-z2", "description": "", "templateType": "anything", "name": "z1minusz2", "group": "Ungrouped variables"}, "im_z3onz4": {"definition": "im(z3/z4)", "description": "", "templateType": "anything", "name": "im_z3onz4", "group": "Ungrouped variables"}, "z2": {"definition": "random(-10..10)+random(-10..10)i", "description": "", "templateType": "anything", "name": "z2", "group": "Ungrouped variables"}, "re_z3onz4": {"definition": "re(z3/z4)", "description": "", "templateType": "anything", "name": "re_z3onz4", "group": "Ungrouped variables"}, "z1z3": {"definition": "z1*z3", "description": "", "templateType": "anything", "name": "z1z3", "group": "Ungrouped variables"}, "modz4sq": {"definition": "z4*z4bar", "description": "", "templateType": "anything", "name": "modz4sq", "group": "Ungrouped variables"}}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

"}, "ungrouped_variables": ["z1", "z2", "z3", "z4", "z4bar", "z3z4bar", "modz4sq", "re_z3onz4", "im_z3onz4", "z1plusz2", "z1minusz2", "z1z3"], "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.

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Given the complex numbers

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\$z_1=\\var{z1},\\quad z_2=\\var{z2}, \\quad z_3=\\var{z3}, \\quad z_4=\\var{z4},\$

\n

\$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}\$

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