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Question

The value of (i+3)100+(i3)100+2100=

A
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B
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C
0
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Solution

The correct option is C 0
(i+3)100+(13)100
(32+i2)2100+((32i2)×2)100
2100(32+i2)+2100(32i2)100
2100(cosπ6+isinπ6)100+cos(π6)+isin(π6)100+1
⎜ ⎜ei50π3+ei50π3+1⎟ ⎟
(2cos(50π3)+1)=2100(2cos(2π2)+1)
= 2100(0)

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