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Simplifying 3(1i + -3) + -7(1i + 3) = 4(2i + -3) Reorder the terms: 3(-3 + 1i) + -7(1i + 3) = 4(2i + -3) (-3 * 3 + 1i * 3) + -7(1i + 3) = 4(2i + -3) (-9 + 3i) + -7(1i + 3) = 4(2i + -3) Reorder the terms: -9 + 3i + -7(3 + 1i) = 4(2i + -3) -9 + 3i + (3 * -7 + 1i * -7) = 4(2i + -3) -9 + 3i + (-21 + -7i) = 4(2i + -3) Reorder the terms: -9 + -21 + 3i + -7i = 4(2i + -3) Combine like terms: -9 + -21 = -30 -30 + 3i + -7i = 4(2i + -3) Combine like terms: 3i + -7i = -4i -30 + -4i = 4(2i + -3) Reorder the terms: -30 + -4i = 4(-3 + 2i) -30 + -4i = (-3 * 4 + 2i * 4) -30 + -4i = (-12 + 8i) Solving -30 + -4i = -12 + 8i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-8i' to each side of the equation. -30 + -4i + -8i = -12 + 8i + -8i Combine like terms: -4i + -8i = -12i -30 + -12i = -12 + 8i + -8i Combine like terms: 8i + -8i = 0 -30 + -12i = -12 + 0 -30 + -12i = -12 Add '30' to each side of the equation. -30 + 30 + -12i = -12 + 30 Combine like terms: -30 + 30 = 0 0 + -12i = -12 + 30 -12i = -12 + 30 Combine like terms: -12 + 30 = 18 -12i = 18 Divide each side by '-12'. i = -1.5 Simplifying i = -1.5
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