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TS EAMCET · Maths · Complex Number

If \(\omega\) is a complex cube root of unity, then \(225+\left(3 \omega+8 \omega^2\right)^2+\left(3 \omega^2+8 \omega\right)^2\) is equal to:

  1. A 72
  2. B 192
  3. C 200
  4. D 248
Verified Solution

Answer & Solution

Correct Answer

(D) 248

Step-by-step Solution

Detailed explanation

\(225+\left(3 \omega+8 \omega^2\right)^2+\left(3 \omega^2+8 \omega\right)^2\) \(=225+9 \omega^2+64 \omega^4+48 \omega^3+9 \omega^4+64 \omega^2+48 \omega^3\) \(=225+9 \omega^2+64 \omega+48+9 \omega+64 \omega^2+48\) \(=225+73\left(\omega^2+\omega\right)+96\)…