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Simplifying z2 + -1(3 + i) * z + a + 2i = 0 Reorder the terms for easier multiplication: z2 + -1z(3 + i) + a + 2i = 0 z2 + (3 * -1z + i * -1z) + a + 2i = 0 Reorder the terms: z2 + (-1iz + -3z) + a + 2i = 0 z2 + (-1iz + -3z) + a + 2i = 0 Reorder the terms: a + 2i + -1iz + -3z + z2 = 0 Solving a + 2i + -1iz + -3z + z2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2i' to each side of the equation. a + 2i + -1iz + -3z + -2i + z2 = 0 + -2i Reorder the terms: a + 2i + -2i + -1iz + -3z + z2 = 0 + -2i Combine like terms: 2i + -2i = 0 a + 0 + -1iz + -3z + z2 = 0 + -2i a + -1iz + -3z + z2 = 0 + -2i Remove the zero: a + -1iz + -3z + z2 = -2i Add 'iz' to each side of the equation. a + -1iz + -3z + iz + z2 = -2i + iz Reorder the terms: a + -1iz + iz + -3z + z2 = -2i + iz Combine like terms: -1iz + iz = 0 a + 0 + -3z + z2 = -2i + iz a + -3z + z2 = -2i + iz Add '3z' to each side of the equation. a + -3z + 3z + z2 = -2i + iz + 3z Combine like terms: -3z + 3z = 0 a + 0 + z2 = -2i + iz + 3z a + z2 = -2i + iz + 3z Add '-1z2' to each side of the equation. a + z2 + -1z2 = -2i + iz + 3z + -1z2 Combine like terms: z2 + -1z2 = 0 a + 0 = -2i + iz + 3z + -1z2 a = -2i + iz + 3z + -1z2 Simplifying a = -2i + iz + 3z + -1z2
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