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Simplifying -4(-4 + I) + 5(1 + 5i) = 0 (-4 * -4 + I * -4) + 5(1 + 5i) = 0 (16 + -4I) + 5(1 + 5i) = 0 16 + -4I + (1 * 5 + 5i * 5) = 0 16 + -4I + (5 + 25i) = 0 Reorder the terms: 16 + 5 + -4I + 25i = 0 Combine like terms: 16 + 5 = 21 21 + -4I + 25i = 0 Solving 21 + -4I + 25i = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -4I + -21 + 25i = 0 + -21 Reorder the terms: 21 + -21 + -4I + 25i = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -4I + 25i = 0 + -21 -4I + 25i = 0 + -21 Combine like terms: 0 + -21 = -21 -4I + 25i = -21 Add '-25i' to each side of the equation. -4I + 25i + -25i = -21 + -25i Combine like terms: 25i + -25i = 0 -4I + 0 = -21 + -25i -4I = -21 + -25i Divide each side by '-4'. I = 5.25 + 6.25i Simplifying I = 5.25 + 6.25i
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