SATHEE: Complex Numbers 5 Question 20

Complex Numbers 5 Question 20

21.

Let $ω = e^{i π / 3}$ and $a, b, c, x, y, z$ be non-zero complex numbers such that $a + b + c = x, a + b ω + c ω^{2} = y$ , $a + b ω^{2} + c ω = z$ .

Then, the value of $\frac{| x |^{2} + | y |^{2} + | z |^{2}}{| a |^{2} + | b |^{2} + | c |^{2}}$ is ……

(2011)

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Answer:

Correct Answer: 21. (3)

Solution:

Priniting error $= e^{i \frac{2 π}{3}}$

Then, $\frac{{| x |^{2} | + | y |}^{2} + | z |^{2}}{(a)^{2} + (b)^{2} + | c |^{2}} = 3$

NOTE Here, $w = e^{i \frac{2 π}{3}}$ , then only integer solution exists.

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