(5+3i)=(u+vi)(u+2i)

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Solution for (5+3i)=(u+vi)(u+2i) equation:


Simplifying
(5 + 3i) = (u + vi)(u + 2i)

Remove parenthesis around (5 + 3i)
5 + 3i = (u + vi)(u + 2i)

Reorder the terms:
5 + 3i = (iv + u)(u + 2i)

Reorder the terms:
5 + 3i = (iv + u)(2i + u)

Multiply (iv + u) * (2i + u)
5 + 3i = (iv(2i + u) + u(2i + u))
5 + 3i = ((2i * iv + u * iv) + u(2i + u))

Reorder the terms:
5 + 3i = ((iuv + 2i2v) + u(2i + u))
5 + 3i = ((iuv + 2i2v) + u(2i + u))
5 + 3i = (iuv + 2i2v + (2i * u + u * u))
5 + 3i = (iuv + 2i2v + (2iu + u2))

Reorder the terms:
5 + 3i = (2iu + iuv + 2i2v + u2)
5 + 3i = (2iu + iuv + 2i2v + u2)

Solving
5 + 3i = 2iu + iuv + 2i2v + u2

Solving for variable 'i'.

Reorder the terms:
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = 2iu + -2iu + iuv + -1iuv + 2i2v + -2i2v + u2 + -1u2

Combine like terms: 2iu + -2iu = 0
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = 0 + iuv + -1iuv + 2i2v + -2i2v + u2 + -1u2
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = iuv + -1iuv + 2i2v + -2i2v + u2 + -1u2

Combine like terms: iuv + -1iuv = 0
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = 0 + 2i2v + -2i2v + u2 + -1u2
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = 2i2v + -2i2v + u2 + -1u2

Combine like terms: 2i2v + -2i2v = 0
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = 0 + u2 + -1u2
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
5 + 3i + -2iu + -1iuv + -2i2v + -1u2 = 0

The solution to this equation could not be determined.

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