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

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Given the complex numbers

\n

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

\n

calculate the following. Enter your answers in the form

\n

\\[x+iy\\]

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$ab=$ [[0]]

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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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No brackets are required or allowed.

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$ac=$ [[0]]

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No brackets are required or allowed.

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$\\frac{a}{b}=$ [[0]]

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What is the complex conjugate of $b$?

\n

$\\overline{b}=$

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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.

\n

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

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No brackets are required or allowed.

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$\\frac{a}{c}=$ [[0]]

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$ad=$ [[0]]

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$\\frac{b}{d}=$ [[0]]

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