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Question

If i=1, then 4+5(12+i32)334+3(12+i32)365 is equal to

A
1i3
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B
1+i3
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C
i3
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D
i3
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Solution

The correct option is C i3
We know that ω=12+32i

Thus, 4+5(12+i32)334+3(12+i32)365

=4+5ω334+3ω365=4+5(ω3)111ω+3(ω3)121ω2

=4+5(1)111ω+3(1)121ω2=4+5ω+3ω2

=1+2ω+3(1+ω+ω2)=1+2ω+3(0)

=1+2ω=11+3i=3i

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