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

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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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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},\\]

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

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\\[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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$z_1+z_2=$

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$z_1-z_2=$

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$z_1z_3=$

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

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