Question

If '$\omega$' is a complex cube root of unity, then $225+(3\omega +8{\omega }^2{)}^2+(3{\omega }^2+8\omega {)}^2=$

• A. 72
• B. 192
• C. 200
• D. 248

Answer 1

The correct option is D 248

$(3\omega +8{\omega }^2)$ $=9{\omega }^2+64{\omega }^4+2.3\omega .8{\omega }^2[{\omega }^3=1]$

$=9{\omega }^2+64\omega +48$

$(3{\omega }^2+8\omega {)}^2$ $=9{\omega }^4+64{\omega }^2+2.3{\omega }^2.8\omega$

$=9\omega +64{\omega }^2+48$

Summing,
$225+(3\omega +8{\omega }^2{)}^2+(3{\omega }^2+8\omega {)}^2$ $=225+9(\omega +{\omega }^2)+64(\omega +{\omega }^2)+96$
$=225-73+96$
$=248$