0

Guest

Courses New

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

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

Question Image
Grade:12

1 Answers

Raghavasimhan
11 Points
6 years ago
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.

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More