Question

solve the following equation and find the values of x and y:

jx/(1+jy) = (3x+j4)/(x+3y)

Answer 1

Answer on Question #57131-Math-Complex Analysis

Solve the following equation and find the values of $x$ and $y$:

$$\frac{jx}{1 + jy} = \frac{3x + j4}{x + 3y}$$

Solution

$$jx(x + 3y) = (3x + j4)(1 + jy)$$ $$j(x^2 + 3xy) = (3x - 4y) + j(3xy + 4)$$ $$\left\{ \begin{array}{l} (3x - 4y) = 0 \\ (x^2 + 3xy) = (3xy + 4) \end{array} \right. \Rightarrow \left\{ \begin{array}{l} y = \frac{3}{4}x \\ x^2 = 4 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} y = \pm \frac{3}{2}. \\ x = \pm 2 \end{array} \right.$$

Answer: $x = \pm 2; y = \pm \frac{3}{2}$.

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