The value of 2 - 3i-4 - 5i is

Standardize the given expression by multiplying with 4 5i 2 + 3i/4 + 5i.4 5i/4 5i = 8 10i + 12i + 15/(4)^2 (5i)^2 = 2i + 23/41 ...

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Algebra of Complex Numbers

The value of ...

Question

The value of $\frac{2 + 3 i}{4 + 5 i}$ is

$\frac{8 + 15 i}{23}$

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$\frac{2 i + 23}{41}$

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3 + 81i

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None of these

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∣ ∣ ∣ ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣ ∣ ∣ ∣

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \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} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

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

\frac{2 + 3 i}{4 + 5 i}

\frac{2 + 5 i}{4 - 3 i}

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