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Simplifying 3a + (4b + 2) * i = 9 + -61 Reorder the terms: 3a + (2 + 4b) * i = 9 + -61 Reorder the terms for easier multiplication: 3a + i(2 + 4b) = 9 + -61 3a + (2 * i + 4b * i) = 9 + -61 Reorder the terms: 3a + (4bi + 2i) = 9 + -61 3a + (4bi + 2i) = 9 + -61 Combine like terms: 9 + -61 = -52 3a + 4bi + 2i = -52 Solving 3a + 4bi + 2i = -52 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4bi' to each side of the equation. 3a + 4bi + -4bi + 2i = -52 + -4bi Combine like terms: 4bi + -4bi = 0 3a + 0 + 2i = -52 + -4bi 3a + 2i = -52 + -4bi Add '-2i' to each side of the equation. 3a + 2i + -2i = -52 + -4bi + -2i Combine like terms: 2i + -2i = 0 3a + 0 = -52 + -4bi + -2i 3a = -52 + -4bi + -2i Divide each side by '3'. a = -17.33333333 + -1.333333333bi + -0.6666666667i Simplifying a = -17.33333333 + -1.333333333bi + -0.6666666667i
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