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Find values for xx and yy if 3x+yi=5x+1+2i3x + yi = 5x + 1 + 2i

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Q. Find values for xx and yy if 3x+yi=5x+1+2i3x + yi = 5x + 1 + 2i
  1. Write Equation and Identify Parts: Write down the given complex equation and identify the real and imaginary parts.\newline3x+yi=5x+1+2i3x + yi = 5x + 1 + 2i
  2. Equate Real and Imaginary Parts: Equate the real parts and the imaginary parts on both sides of the equation.\newlineReal parts: 3x=5x+13x = 5x + 1\newlineImaginary parts: yi=2iyi = 2i
  3. Solve for x: Solve the real part equation for x.\newline3x=5x+13x = 5x + 1\newline3x−5x=13x - 5x = 1\newline−2x=1-2x = 1\newlinex=1/−2x = 1 / -2\newlinex=−1/2x = -1/2
  4. Solve for yy: Solve the imaginary part equation for yy.yi=2iyi = 2iSince ii is the imaginary unit, we can equate the coefficients of ii.y=2y = 2

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