Complex Numbers And Quadratic Equations question 240
Question: If $ \alpha $ and $ \beta $ are imaginary cube roots of unity, then $ {{\alpha }^{4}}+{{\beta }^{4}} $ + $ \frac{1}{\alpha \beta }= $ [IIT 1977]
Options:
A) 3
B) 0
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
Complex cube root of unity are $ 1,\omega ,{{\omega }^{2}} $ Let $ \alpha =\omega ,\beta ={{\omega }^{2}} $ ; Then $ {{\alpha }^{4}}+{{\beta }^{4}}+{{\alpha }^{-1}}{{\beta }^{-1}} $ $ ={{\omega }^{4}}+{{({{\omega }^{2}})}^{4}}+({{\omega }^{-1}}){{({{\omega }^{2}})}^{-1}}=\omega +{{\omega }^{2}}+1=0 $ .
BETA
