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JEE Advanced 2011Paper 2
Exam
JEE Advanced
Year
2011
Paper
Paper 2
Subject
Mathematics
Chapter
Complex Number

JEE Advanced 2011 · Paper 2 · Mathematics · Complex Number

Let ω=e^ i π / 3 and a, b, c, x, y, z be non-zero complex numbers...

Let ω=eiπ/3\omega=e^{i \pi / 3} and a,b,c,x,y,za, b, c, x, y, z be non-zero complex numbers such that a+b+c=x,a+bω+cω2=y,a+bω2+cω=za+b+c=x, a+b \omega+c \omega^2=y, a+b \omega^2+c \omega=z. Then, the value of ∣x∣2+∣y∣2+∣z∣2∣a∣2+∣b∣2+∣c∣2\frac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2} is

Correct answer

0

Step-by-step solution

Here, ω=ei2π/3\omega=e^{i 2 \pi / 3}, then only integer solution exists. Then, ∣x2∣+∣y2∣+∣z2∣∣a2∣+∣b2∣+∣c2∣=3\frac{\left|x^2\right|+\left|y^2\right|+\left|z^2\right|}{\left|a^2\right|+\left|b^2\right|+\left|c^2\right|}=3
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