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Question

If (3+i)100=299(p+iq), then p and q are roots of the equation

A
x2(31)x3=0
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B
x2+(31)x3=0
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C
x2(3+1)x+3=0
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D
x2+(3+1)x+3=0
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Solution

The correct option is A x2(31)x3=0
(3+i)100=299(p+iq)
(2eiπ6)100=299(p+iq)
2ei50π3=p+iq
2ei16π+2π3=p+iq
2(cos2π3+isin2π3)=p+iq
p=1, q=3
Equation with roots 1 and 3 is
x2(31)x3=0

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