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If (x+iy)(2−3i)=4+i then (x, y) =

A. (1, 1/13 )
B. ( - 5/13, 14/13 )
C. ( 5/13, 14/13 )
D. ( - 5/13, 14/13 )

User Shawnay
by
8.5k points

1 Answer

4 votes

Final answer:

By expanding the product of the given complex numbers and equating real and imaginary parts, we find the solution (x, y) = (-5/13, 14/13), which corresponds to option B.

Step-by-step explanation:

To find the values of x and y in the complex number equation (x+iy)(2−3i)=4+i, we need to expand the product on the left side and then equate the real and imaginary parts with those on the right side.

Expanding the product, we have:

  • (x × 2) + (x × -3i) + (iy × 2) + (iy × -3i) = 4 + i
  • (2x - 3ix + 2iy - 3y) = 4 + i

Combining like terms, we get:

  • Real part: 2x - 3y = 4
  • Imaginary part: 2y - 3x = 1

Solving these two equations simultaneously for x and y, we find the solution that matches one of the given options.

Option B provides the solution: (x, y) = (-5/13, 14/13), which is the correct answer.

User Strattonn
by
8.8k points
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