Question

In triangle ABC, z = $\left| \begin{matrix} e^{- 2iA} & e^{+ ic} & e^{iB} \\ e^{iC} & e^{- i2B} & e^{iA} \\ e^{iB} & e^{iA} & e^{- i2C} \end{matrix} \right|$ where i = $\sqrt{- 1}$. Then arg(z) =

• A. 0
• B. Does not exist
• C. p
• D. None of these

Answer 1

Answer: (C)

p

Answer 2

z = e^–2iA(e^–2i(B+C) – e^2iA) – e^+ic(e^–ic – e^{i(A + B)})+ e^iB(e^i(A+C) – e^–iB)

z = e^–2pi – 1 – 1 + e^pi + e^ip – 1 = 1 – 1 – 1 – 1 – 1 – 1 = – 4 Ž arg(z) = 11