(x+3i)=(4-i)+(5-4yi)

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Solution for (x+3i)=(4-i)+(5-4yi) equation:


Simplifying
(x + 3i) = (4 + -1i) + (5 + -4yi)

Reorder the terms:
(3i + x) = (4 + -1i) + (5 + -4yi)

Remove parenthesis around (3i + x)
3i + x = (4 + -1i) + (5 + -4yi)

Remove parenthesis around (4 + -1i)
3i + x = 4 + -1i + (5 + -4yi)

Remove parenthesis around (5 + -4iy)
3i + x = 4 + -1i + 5 + -4iy

Reorder the terms:
3i + x = 4 + 5 + -1i + -4iy

Combine like terms: 4 + 5 = 9
3i + x = 9 + -1i + -4iy

Solving
3i + x = 9 + -1i + -4iy

Solving for variable 'i'.

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

Add 'i' to each side of the equation.
3i + i + x = 9 + -1i + i + -4iy

Combine like terms: 3i + i = 4i
4i + x = 9 + -1i + i + -4iy

Combine like terms: -1i + i = 0
4i + x = 9 + 0 + -4iy
4i + x = 9 + -4iy

Add '4iy' to each side of the equation.
4i + 4iy + x = 9 + -4iy + 4iy

Combine like terms: -4iy + 4iy = 0
4i + 4iy + x = 9 + 0
4i + 4iy + x = 9

Add '-1x' to each side of the equation.
4i + 4iy + x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
4i + 4iy + 0 = 9 + -1x
4i + 4iy = 9 + -1x

Reorder the terms:
-9 + 4i + 4iy + x = 9 + -1x + -9 + x

Reorder the terms:
-9 + 4i + 4iy + x = 9 + -9 + -1x + x

Combine like terms: 9 + -9 = 0
-9 + 4i + 4iy + x = 0 + -1x + x
-9 + 4i + 4iy + x = -1x + x

Combine like terms: -1x + x = 0
-9 + 4i + 4iy + x = 0

The solution to this equation could not be determined.

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