We have to find x and y given that (8x + yi) / (1 + 4i) = (2x + i)/ (3 + 2i)
(8x + yi) / (1 + 4i) = (2x + i)/ (3 + 2i)
=> (8x + yi) (3 + 2i) = (2x +i) (1+ 4i)
=> 24x + 16xi + 3yi + 2yi^2 = 2x + i + 8xi + 4i^2
=> 24x + 16xi + 3yi – 2y = 2x + i + 8xi – 4
=> 24x – 2y + i (16x + 3y) = 2x – 4 + i (8x +1)
Equate the real and complex coefficients
We get 24x – 2y = 2x – 4
22x – 2y = -4
=> 11x – y = -2
=> y = 11x + 2
and 16x + 3y = 8x + 1
=> 8x + 3y – 1 = 0
substitute y = 11x + 2
=> 8x + 33x + 6 – 1 = 0
=> 41x = -5
=> x = -5/41
y = 11*(-5/41) + 2
=> (-55 + 82)/41
=> 27 / 41
Therefore x = -5/41 and y = 27/41
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