3+4i=(x+yi)(1+i)

Solution for 3+4i=(x+yi)(1+i) equation:

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

Reorder the terms:
3 + 4i = (iy + x)(1 + i)

Multiply (iy + x) * (1 + i)
3 + 4i = (iy(1 + i) + x(1 + i))
3 + 4i = ((1 * iy + i * iy) + x(1 + i))
3 + 4i = ((1iy + i2y) + x(1 + i))
3 + 4i = (1iy + i2y + (1 * x + i * x))

Reorder the terms:
3 + 4i = (1iy + i2y + (ix + 1x))
3 + 4i = (1iy + i2y + (ix + 1x))

Reorder the terms:
3 + 4i = (ix + 1iy + i2y + 1x)
3 + 4i = (ix + 1iy + i2y + 1x)

Solving
3 + 4i = ix + 1iy + i2y + 1x

Solving for variable 'i'.

Reorder the terms:
3 + 4i + -1ix + -1iy + -1i2y + -1x = ix + -1ix + 1iy + -1iy + i2y + -1i2y + 1x + -1x

Combine like terms: ix + -1ix = 0
3 + 4i + -1ix + -1iy + -1i2y + -1x = 0 + 1iy + -1iy + i2y + -1i2y + 1x + -1x
3 + 4i + -1ix + -1iy + -1i2y + -1x = 1iy + -1iy + i2y + -1i2y + 1x + -1x

Combine like terms: 1iy + -1iy = 0
3 + 4i + -1ix + -1iy + -1i2y + -1x = 0 + i2y + -1i2y + 1x + -1x
3 + 4i + -1ix + -1iy + -1i2y + -1x = i2y + -1i2y + 1x + -1x

Combine like terms: i2y + -1i2y = 0
3 + 4i + -1ix + -1iy + -1i2y + -1x = 0 + 1x + -1x
3 + 4i + -1ix + -1iy + -1i2y + -1x = 1x + -1x

Combine like terms: 1x + -1x = 0
3 + 4i + -1ix + -1iy + -1i2y + -1x = 0

The solution to this equation could not be determined.