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Question

If ω=1+3i2, then 3+ω+3ω24 is


A

16

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B

-16

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C

16ω

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D

16ω2

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Solution

The correct option is C

16ω


Explanation for the correct answer:

Step 1 : Information required for the question

We know that the cube root of unity is given by ω3=1.

Also, 1+ω+ω2=0 and from this equation we have,

1+ω2=-ω1

Step 2 : Calculation of the given term

First, simplify the expression 3+ω+3ω24,

3+ω+3ω24=31+ω2+ω4=-3ω+ω4from1=-2ω4=16ω4=16ω·ω3ω3=1=16ω

Hence, the correct option is (C)


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