// Numbas version: exam_results_page_options {"name": "Arithmetics of complex numbers II", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "
Multiplication and addition of complex numbers. Four parts.
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\nInput all numbers as fractions or integers. Also do not include brackets in your answers.
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\nThe solution is given by:
\n
$\\simplify[std]{{e6*i}}(\\simplify[std]{{a}})=\\simplify[std]{{a*e6*i}}$
b)
$\\simplify[std]{{a}*{z4}={a*z4}}$
\n
c)
\\[ \\begin{eqnarray*} \\simplify[std,!otherNumbers]{{a}*({a3} + {b3} * i + {c3} * i ^ 2 + {d3} * i ^ 3)}&=&\\simplify[std]{{a}*{a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3}}\\\\ &=&\\simplify[std]{{a*(a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3)}} \\end{eqnarray*} \\]
d)
This can be calculated by using the formula twice, firstly to multiply out the first two sets of parentheses,
\nand then to multiply the result of that calculation by the third set of parentheses.
\nSo we obtain:
\\[ \\begin{eqnarray*} (\\var{a})(\\var{z1})(\\var{z3})&=&((\\var{a})(\\var{z1}))(\\var{z3})\\\\ &=&(\\var{a*(z1)})(\\var{z3})\\\\ &=&\\var{a*(z1)*(z3)} \\end{eqnarray*} \\]