Complex Numbers 5 Question 20
21. Let $\omega=e^{i \pi / 3}$ and $a, b, c, x, y, z$ be non-zero complex numbers such that $a+b+c=x, a+b \omega+c \omega^{2}=y$, $a+b \omega^{2}+c \omega=z$.
Then, the value of $\frac{|x|^{2}+|y|^{2}+|z|^{2}}{|a|^{2}+|b|^{2}+|c|^{2}}$ is ……
(2011)
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Solution:
- Priniting error $=e^{i \frac{2 \pi}{3}}$
Then, $\frac{\left.|x|^{2}|+| y\right|^{2}+|z|^{2}}{(a)^{2}+(b)^{2}+|c|^{2}}=3$
NOTE Here, $w=e^{i \frac{2 \pi}{3}}$, then only integer solution exists.
