Question

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 - i²b²) - (i² d² - c²)
= (a² +b²) - (- d² - c²) [ $because$ i² = - 1 ]
= (a² +b² +c² + d²)

Question

Wired Faculty App

Evaluate

$open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar$

Solution

Let $increment space equals space open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar$ = (2) (2) - (4) (- 1) = 4 + 4 = 8

Question

Wired Faculty App

Evaluate $open vertical bar table row 2 cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar$

Solution

Let $increment equals open vertical bar table row cell space space space 2 end cell cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar$ =(2) (- 1) - (4) (- 5) = - 2 + 20 = 18

Question

Wired Faculty App

Evaluate $open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar$

Solution

$increment equals open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar$
=(x) (x) - (x + 1) (x - 1) (x - 1) = x² - (x²- 1) = x² - x² + 1 = 1

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Inverse Trigonometric Functions

Evaluates :

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

Evaluate

$open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar$

Evaluate $open vertical bar table row 2 cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar$

Evaluate $open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar$

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