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Simplifying (5 + -3i) * 3 = a + ib Reorder the terms for easier multiplication: 3(5 + -3i) = a + ib (5 * 3 + -3i * 3) = a + ib (15 + -9i) = a + ib Solving 15 + -9i = a + bi Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1bi' to each side of the equation. 15 + -1bi + -9i = a + bi + -1bi Combine like terms: bi + -1bi = 0 15 + -1bi + -9i = a + 0 15 + -1bi + -9i = a Add '-15' to each side of the equation. 15 + -1bi + -15 + -9i = -15 + a Reorder the terms: 15 + -15 + -1bi + -9i = -15 + a Combine like terms: 15 + -15 = 0 0 + -1bi + -9i = -15 + a -1bi + -9i = -15 + a Reorder the terms: 15 + -1a + -1bi + -9i = -15 + a + 15 + -1a Reorder the terms: 15 + -1a + -1bi + -9i = -15 + 15 + a + -1a Combine like terms: -15 + 15 = 0 15 + -1a + -1bi + -9i = 0 + a + -1a 15 + -1a + -1bi + -9i = a + -1a Combine like terms: a + -1a = 0 15 + -1a + -1bi + -9i = 0 The solution to this equation could not be determined.
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