Question

Evaluates :
$open vertical bar table row cell straight a plus ib end cell cell straight c plus id end cell row cell negative straight c plus ic end cell cell straight a minus ib end cell end table close vertical bar$

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Solution

open vertical bar table row cell straight a plus ib end cell cell straight c plus id end cell row cell negative straight c plus ic end cell cell straight a minus ib end cell end table close vertical bar space equals space left parenthesis straight a plus ib right parenthesis left parenthesis straight a minus ib right parenthesis minus left parenthesis straight c plus id right parenthesis left parenthesis straight c minus id right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight a squared minus straight i squared straight b squared right parenthesis minus left parenthesis straight i squared space straight d to the power of 2 space space end exponent minus straight c squared right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets table row because cell straight i squared space equals space minus 1 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight a squared plus straight b squared right parenthesis space minus left parenthesis negative straight d squared minus straight c squared right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals straight a squared plus straight b squared space plus straight c to the power of 2 space end exponent plus straight d squared space space space space space space space space space space space space

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Determinants

Evaluates :
$open vertical bar table row cell straight a plus ib end cell cell straight c plus id end cell row cell negative straight c plus ic end cell cell straight a minus ib end cell end table close vertical bar$

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