Complex Numbers And Quadratic Equations question 843
Question: If $ {e^{i\theta }}=\cos \theta +i\sin \theta $ , then in $ \Delta ABC $ value of $ e^{iA}.e^{iB}.e^{iC} $ is [AMU 2005]
Options:
A) -i
B) 1
C) -1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ e^{iA}.e^{iB}.e^{iC}={e^{iA+iB+iC}}={e^{i(A+B+C)}}={e^{i\pi }} $ [ $ \therefore A+B+C=\pi $ ] = $ \cos \pi +i\sin \pi =(-1)+i(0)=-1 $ .
BETA
