// Numbas version: exam_results_page_options {"name": "Inbbavathie's copy of Complex number arithmetic: multiply and divide", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Inbbavathie's copy of Complex number arithmetic: multiply and divide", "statement": "

Given the complex numbers

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\\[a=\\var{a},\\quad b=\\var{b},\\quad c=\\var{c},\\quad d=\\var{d},\\]

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calculate the following. Enter your answers in the form

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\\[x+iy\\] Express your answers in 2 decimal places.

", "advice": "

\\[z_1+z_2=(\\var{z1})+(\\var{z2})=\\simplify{{z1}+{z2}}\\]

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\\[z_1-z_2=(\\var{z1})-(\\var{z2})=\\simplify{{z1}-{z2}}\\]

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\\[z_1z_3=(\\var{z1})(\\var{z3})=\\var{z1z3}\\]

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\\[\\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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No brackets are required or allowed.

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$ab=$

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Expand the brackets $(\\var{a})(\\var{b})$.

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Simplify using the fact $i^2=-1$.

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$ac=$

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No brackets are required or allowed.

", "partialCredit": 0, "showStrings": false, "strings": ["(", ")"]}, "vsetrange": [0, 1]}, {"showCorrectAnswer": true, "notallowed": {"message": "

No brackets are required or allowed.

", "partialCredit": 0, "showStrings": false, "strings": ["(", ")"]}, "scripts": {}, "checkingtype": "absdiff", "answer": "{a/b}", "stepsPenalty": 0, "expectedvariablenames": [], "variableReplacements": [], "vsetrangepoints": 5, "prompt": "

$\\frac{a}{b}=$

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What is the complex conjugate of $b$?

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$\\overline{b}=$

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Multiply the numerator ($\\var{a}$) by $\\overline{b}$.

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Multiply the denominator ($\\var{b}$) by $\\overline{b}$.

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Now divide your two answers.

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\\[\\frac{a}{b}=\\frac{a\\overline{b}}{b\\overline{b}}\\]

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$\\frac{a}{c}=$

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No brackets are required or allowed.

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

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