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Simplifying 21i + 42 = 22i + 33 Reorder the terms: 42 + 21i = 22i + 33 Reorder the terms: 42 + 21i = 33 + 22i Solving 42 + 21i = 33 + 22i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-22i' to each side of the equation. 42 + 21i + -22i = 33 + 22i + -22i Combine like terms: 21i + -22i = -1i 42 + -1i = 33 + 22i + -22i Combine like terms: 22i + -22i = 0 42 + -1i = 33 + 0 42 + -1i = 33 Add '-42' to each side of the equation. 42 + -42 + -1i = 33 + -42 Combine like terms: 42 + -42 = 0 0 + -1i = 33 + -42 -1i = 33 + -42 Combine like terms: 33 + -42 = -9 -1i = -9 Divide each side by '-1'. i = 9 Simplifying i = 9
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