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Simplifying 4(I + -3) + -1i = I + -6 Reorder the terms: 4(-3 + I) + -1i = I + -6 (-3 * 4 + I * 4) + -1i = I + -6 (-12 + 4I) + -1i = I + -6 Reorder the terms: -12 + 4I + -1i = -6 + I Solving -12 + 4I + -1i = -6 + I 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. -12 + 4I + -1I + -1i = -6 + I + -1I Combine like terms: 4I + -1I = 3I -12 + 3I + -1i = -6 + I + -1I Combine like terms: I + -1I = 0 -12 + 3I + -1i = -6 + 0 -12 + 3I + -1i = -6 Add '12' to each side of the equation. -12 + 3I + 12 + -1i = -6 + 12 Reorder the terms: -12 + 12 + 3I + -1i = -6 + 12 Combine like terms: -12 + 12 = 0 0 + 3I + -1i = -6 + 12 3I + -1i = -6 + 12 Combine like terms: -6 + 12 = 6 3I + -1i = 6 Add 'i' to each side of the equation. 3I + -1i + i = 6 + i Combine like terms: -1i + i = 0 3I + 0 = 6 + i 3I = 6 + i Divide each side by '3'. I = 2 + 0.3333333333i Simplifying I = 2 + 0.3333333333i
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