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Grade: 12

                        

Give the answer fast please(complex numbers) Not getting the right answer after half the way

2 years ago

Answers : (1)

Raghavasimhan
11 Points
							The given numbers are complex cube roots of unity.[ (-1+i√3)/2]^26 is (ω²)^26 and [(-1-i√3)/2]^26 is ω^26. 2×26=52 which leaves remainder 1 and 26 leaves remainder 2 when divided by 3. We know that the cube roots of unity repeat themselves every 3rd power(ω³,ω^6,ω^9 etc all are equal to one). Hence, the problem reduces to ω+ω². But we know,1+ω+ω²=0=>ω+ω²=-1 is the answer to the problem.
						
2 years ago
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