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Simplifying z2 + (1 + 4i) + -1(5 + i) = 0 Remove parenthesis around (1 + 4i) z2 + 1 + 4i + -1(5 + i) = 0 z2 + 1 + 4i + (5 * -1 + i * -1) = 0 z2 + 1 + 4i + (-5 + -1i) = 0 Reorder the terms: 1 + -5 + 4i + -1i + z2 = 0 Combine like terms: 1 + -5 = -4 -4 + 4i + -1i + z2 = 0 Combine like terms: 4i + -1i = 3i -4 + 3i + z2 = 0 Solving -4 + 3i + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 3i + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + 3i + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3i + z2 = 0 + 4 3i + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 3i + z2 = 4 Add '-1z2' to each side of the equation. 3i + z2 + -1z2 = 4 + -1z2 Combine like terms: z2 + -1z2 = 0 3i + 0 = 4 + -1z2 3i = 4 + -1z2 Divide each side by '3'. i = 1.333333333 + -0.3333333333z2 Simplifying i = 1.333333333 + -0.3333333333z2
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