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Simplifying z4 + -3(1 + 2i) + -8 + -6i = 0 z4 + (1 * -3 + 2i * -3) + -8 + -6i = 0 z4 + (-3 + -6i) + -8 + -6i = 0 Reorder the terms: -3 + -8 + -6i + -6i + z4 = 0 Combine like terms: -3 + -8 = -11 -11 + -6i + -6i + z4 = 0 Combine like terms: -6i + -6i = -12i -11 + -12i + z4 = 0 Solving -11 + -12i + z4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '11' to each side of the equation. -11 + -12i + 11 + z4 = 0 + 11 Reorder the terms: -11 + 11 + -12i + z4 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -12i + z4 = 0 + 11 -12i + z4 = 0 + 11 Combine like terms: 0 + 11 = 11 -12i + z4 = 11 Add '-1z4' to each side of the equation. -12i + z4 + -1z4 = 11 + -1z4 Combine like terms: z4 + -1z4 = 0 -12i + 0 = 11 + -1z4 -12i = 11 + -1z4 Divide each side by '-12'. i = -0.9166666667 + 0.08333333333z4 Simplifying i = -0.9166666667 + 0.08333333333z4
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