AP EAMCET · Maths · Complex Number
If \(\omega\) is a complex cube root of unity, the \(\left[\frac{51+73 \omega+87 \omega^2}{73+87 \omega+51 \omega^2}+\frac{51+73 \omega+87 \omega^2}{87+51 \omega+73 \omega^2}\right]=\)
- A 1
- B -1
- C 0
- D 2
Answer & Solution
Correct Answer
(B) -1
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left[\frac{51+73 \omega+87 \omega^2}{73+87 \omega+51 \omega^2}+\frac{51+73 \omega+87 \omega^2}{87+51 \omega+73 \omega^2}\right]^{15} \\ & =\left[\begin{array}{c}\frac{51 \omega^2+73 \omega^3+87 \omega^4}{73+87 \omega+51 \omega^2} \times \frac{1}{\omega^2} \\…
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