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Simplifying 4 + 5i = z + -1(1 + -1i) 4 + 5i = z + (1 * -1 + -1i * -1) 4 + 5i = z + (-1 + 1i) Reorder the terms: 4 + 5i = -1 + 1i + z Solving 4 + 5i = -1 + 1i + z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. 4 + 5i + -1i = -1 + 1i + -1i + z Combine like terms: 5i + -1i = 4i 4 + 4i = -1 + 1i + -1i + z Combine like terms: 1i + -1i = 0 4 + 4i = -1 + 0 + z 4 + 4i = -1 + z Add '-4' to each side of the equation. 4 + -4 + 4i = -1 + -4 + z Combine like terms: 4 + -4 = 0 0 + 4i = -1 + -4 + z 4i = -1 + -4 + z Combine like terms: -1 + -4 = -5 4i = -5 + z Divide each side by '4'. i = -1.25 + 0.25z Simplifying i = -1.25 + 0.25z
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