Given - - -1 2-3i 5-4i- 2-3i 8 1-i- 5-4i 1-i 3- - -Without expanding prove that is real-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Properties of Determinants

Given = |...

Question

Given $△ =$ $∣ ∣ ∣ ∣ \begin{matrix} - 1 & 2 + 3 i & 5 - 4 i 2 - 3 i & 8 & 1 + i 5 + 4 i & 1 - i & 3 \end{matrix} ∣ ∣ ∣ ∣$

Without expanding prove that $△$ is real.

Open in App

Solution

Suggest Corrections

Similar questions

(\frac{1}{1 - 4 i} - \frac{2}{1 + i}) (\frac{3 - 4 i}{5 + i})

(\frac{1}{1 - 4 i} - \frac{2}{1 + i}) (\frac{3 - 4 i}{5 + i})

A

A = ⎡ ⎢ ⎣ \begin{matrix} 2 + 3 i & 2 & 5 - 3 - i & 7 & 3 - i 3 - 2 i & i & 2 + i \end{matrix} ⎤ ⎥ ⎦

A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2 & - \frac{1}{2} + \frac{i}{2} & m + k i - \frac{1}{2} - \frac{i}{2} & 7 & \frac{3}{2} - 1 4 - i & \frac{3}{2} + 1 & 2 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ + ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 3 i & \frac{5}{2} - \frac{i}{2} & n + p i - \frac{5}{2} - \frac{i}{2} & 0 & \frac{3}{2} - 1 - i & - \frac{3}{2} & i \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

m + k + n + p

∣ ∣ ∣ ∣ ∣ \begin{matrix} - 5 & 3 + 5 i & \frac{3}{2} - 4 i 3 - 5 i & 8 & 4 + 5 i \frac{3}{2} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

Join BYJU'S Learning Program