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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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