Find the values of x and y , if 2 x + 3yi = 2+ 12i , where ` x, y in R`

Explanation

To solve the equation \( 2x + 3yi = 2 + 12i \), where \( x \) and \( y \) are real numbers, we can follow these steps:

### Step 1: Identify the real and imaginary parts
The equation can be separated into its real and imaginary components. On the left side, the real part is \( 2x \) and the imaginary part is \( 3y \). On the right side, the real part is \( 2 \) and the imaginary part is \( 12 \).

### Step 2: Set up equations
From the real parts, we have:
\[
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