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Simplifying (3 + 7i)(-5 + -2i) = -1 + -41i Multiply (3 + 7i) * (-5 + -2i) (3(-5 + -2i) + 7i * (-5 + -2i)) = -1 + -41i ((-5 * 3 + -2i * 3) + 7i * (-5 + -2i)) = -1 + -41i ((-15 + -6i) + 7i * (-5 + -2i)) = -1 + -41i (-15 + -6i + (-5 * 7i + -2i * 7i)) = -1 + -41i (-15 + -6i + (-35i + -14i2)) = -1 + -41i Combine like terms: -6i + -35i = -41i (-15 + -41i + -14i2) = -1 + -41i Add '41i' to each side of the equation. -15 + -41i + 41i + -14i2 = -1 + -41i + 41i Combine like terms: -41i + 41i = 0 -15 + 0 + -14i2 = -1 + -41i + 41i -15 + -14i2 = -1 + -41i + 41i Combine like terms: -41i + 41i = 0 -15 + -14i2 = -1 + 0 -15 + -14i2 = -1 Solving -15 + -14i2 = -1 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -14i2 = -1 + 15 Combine like terms: -15 + 15 = 0 0 + -14i2 = -1 + 15 -14i2 = -1 + 15 Combine like terms: -1 + 15 = 14 -14i2 = 14 Divide each side by '-14'. i2 = -1 Simplifying i2 = -1 Reorder the terms: 1 + i2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + i2 = 0 The solution to this equation could not be determined.
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