CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$\mathrm{z}(z\neq 0)$$ p,q,r are distinct cube roots of a complex number and $$\mathrm{a}$$, b,c are complex numbers such that $$ap+bq+cr\neq 0$$ 
then $$\displaystyle \frac{(aq+br+cp)(ar+bp+cq)}{(ap+bq+cr)^{2}}=?$$


A
1
loader
B
1
loader
C
abc
loader
D
pqr
loader

Solution

The correct option is A $$1$$
We know that $$1, w$$ and $$w^2$$ are cube roots of unity.
Thus, cube roots of any number $$k^3$$ will be $$k, kw$$ and $$kw^2.$$
Now substituting these values for $$p,q$$ and $$r $$ respectively and using $$w^3 = 1, $$
numerator becomes $$k^2 \times (aw + bw^2 + c)(aw^2 + b + cw) = k^2(a^2 + abw + acw^2 + abw + b^2w^2 + bc + acw^2 + bc + c^2w)$$
Denominator becomes $$k^2 (c^2w + a^2 + abw + acw^2 + abw + b^2w^2 + bc + acw^2 + bc)$$
Thus observing, the numerator and denominator are the same.
Hence answer becomes 1.  

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image