(X+yi)(1-2i)=7-4i

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Solution for (X+yi)(1-2i)=7-4i equation: 


Simplifying
(X + yi)(1 + -2i) = 7 + -4i

Multiply (X + iy) * (1 + -2i)
(X(1 + -2i) + iy(1 + -2i)) = 7 + -4i
((1 * X + -2i * X) + iy(1 + -2i)) = 7 + -4i
((1X + -2iX) + iy(1 + -2i)) = 7 + -4i
(1X + -2iX + (1 * iy + -2i * iy)) = 7 + -4i
(1X + -2iX + (1iy + -2i2y)) = 7 + -4i
(1X + -2iX + 1iy + -2i2y) = 7 + -4i

Solving
1X + -2iX + 1iy + -2i2y = 7 + -4i

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-1iy' to each side of the equation.
1X + -2iX + 1iy + -1iy + -2i2y = 7 + -4i + -1iy

Combine like terms: 1iy + -1iy = 0
1X + -2iX + 0 + -2i2y = 7 + -4i + -1iy
1X + -2iX + -2i2y = 7 + -4i + -1iy

Add '2i2y' to each side of the equation.
1X + -2iX + -2i2y + 2i2y = 7 + -4i + -1iy + 2i2y

Combine like terms: -2i2y + 2i2y = 0
1X + -2iX + 0 = 7 + -4i + -1iy + 2i2y
1X + -2iX = 7 + -4i + -1iy + 2i2y

Reorder the terms:
-7 + 1X + 4i + -2iX + iy + -2i2y = 7 + -4i + -1iy + 2i2y + -7 + 4i + iy + -2i2y

Reorder the terms:
-7 + 1X + 4i + -2iX + iy + -2i2y = 7 + -7 + -4i + 4i + -1iy + iy + 2i2y + -2i2y

Combine like terms: 7 + -7 = 0
-7 + 1X + 4i + -2iX + iy + -2i2y = 0 + -4i + 4i + -1iy + iy + 2i2y + -2i2y
-7 + 1X + 4i + -2iX + iy + -2i2y = -4i + 4i + -1iy + iy + 2i2y + -2i2y

Combine like terms: -4i + 4i = 0
-7 + 1X + 4i + -2iX + iy + -2i2y = 0 + -1iy + iy + 2i2y + -2i2y
-7 + 1X + 4i + -2iX + iy + -2i2y = -1iy + iy + 2i2y + -2i2y

Combine like terms: -1iy + iy = 0
-7 + 1X + 4i + -2iX + iy + -2i2y = 0 + 2i2y + -2i2y
-7 + 1X + 4i + -2iX + iy + -2i2y = 2i2y + -2i2y

Combine like terms: 2i2y + -2i2y = 0
-7 + 1X + 4i + -2iX + iy + -2i2y = 0

The solution to this equation could not be determined.

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