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Inverse Trigonometric Functions

Question
CBSEENMA12032611
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Evaluates :

open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar

Solution

Consider open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar = (a + i b) (a - i b)-(c + i b)(- c + i d)
                                            = (a2 - i2 b2 ) - (i2 d2 - c2)
                                            = (a2 + b2 ) - (- d2 - c2)                        [ because i2 = - 1 ]
                                            = (a2 + b2 + c2 + d2)  
                                          

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