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Unraveling Complex Roots with the Quadratic Formula Answers needed

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Finding the Roots of x² + (2 - 3i)x - 6i = 0: A Journey into Complex Numbers

The equation x² + (2 - 3i)x - 6i = 0 beckons us to delve into the fascinating realm of complex numbers. These numbers, unlike their real counterparts, embrace the concept of the imaginary unit "i", defined as the square root of -1. Solving such equations requires venturing beyond the confines of simple arithmetic and employing powerful tools like the quadratic formula and complex conjugates.

The term under the square root, b² - 4ac, is called the discriminant. It holds the key to unlocking the nature of the roots. If the discriminant is:

• Positive: There are two distinct real roots.

Since the discriminant is positive (13), we can expect two distinct real roots.

Step 3: Conjuring the Roots with the Formula

Step 4: Unveiling the Roots

Simplifying these expressions, we arrive at the roots:

• x₂ = (-1 + 3i - √(13)) / 2 = (-1 + 3i - √(13) + 0i) / 2 = (-1 + 2i - √(13)) / 2

Step 5: A Final Reflection