Find the value of $x$ and , if $(x + 2 y) + i (2 x - 3 y)$ is the conjugate of $5 + 4 i .$

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Solution

$\begin{matrix} C o n j u g a t e o f 5 + 4 i i s 5 - 4 i (x + 2 y) + i (2 x - 3 y) = 5 - 4 i \begin{matrix} x + 2 y = 5.... (i) 2 x - 3 y = - 4...... (i i) 2 x + 4 y = 10..... (i i i) m u l t i p l y (i) b y 2 \end{matrix} - ---------------------------------------- - - 7 y = - 14 x = 1 y = 2 \end{matrix}$

Hence, this is the answer.

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