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\\[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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$z_1+z_2=$

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$z_4z_3=$

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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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\n

Given the complex numbers

\n

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

\n

calculate the following (write your answers in Cartesian/rectangular form).

", "variable_groups": [{"variables": ["z3bar", "z2bar", "z1bar", "z4bar"], "name": "Unnamed group"}, {"variables": ["modz2sq", "modz1sq", "modz3sq", "modz4sq"], "name": "Unnamed group"}, {"variables": ["z3z4bar", "z2z4bar"], "name": "Unnamed group"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"im_z3onz4": {"definition": "im(z3/z4)", "templateType": "anything", "group": "Ungrouped variables", "name": "im_z3onz4", "description": ""}, "z1z3": {"definition": "z1*z3", "templateType": "anything", "group": "Ungrouped variables", "name": "z1z3", "description": ""}, "z1z2": {"definition": "z1*z2", "templateType": "anything", "group": "Ungrouped variables", "name": "z1z2", "description": "

z1z2

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

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