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Question

If 'ω' is a complex cube root of unity, then 225+(3ω+8ω2)2+(3ω2+8ω)2=

A
72
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B
192
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C
200
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D
248
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Solution

The correct option is D 248
(3ω+8ω2) =9ω2+64ω4+2.3ω.8ω2[ω3=1]
=9ω2+64ω+48
(3ω2+8ω)2 =9ω4+64ω2+2.3ω2.8ω
=9ω+64ω2+48

Summing,
225+(3ω+8ω2)2+(3ω2+8ω)2 =225+9(ω+ω2)+64(ω+ω2)+96
=22573+96
=248

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