Complex Numbers - Roots

Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths.

The following diagram explains complex conjugate pairs. Scroll down the page for more examples and solutions.

 

Complex Numbers: Roots of a quadratic equation - conjugate pairs
If the roots of a quadratic equation are complex then they are always a complex conjugate pair.
Examples:

1. Find the quadratic equation that has 5 - 3i as one of its roots.
2. Find the quadratic equation that has -4 + 2i as one of its roots.

Complex Numbers: Roots of a cubic equation
Examples:

1. Find all the roots of the equation x³ - 4x² + x + 26 = 0
2. Find all the roots of the equation x³ - 7x² + 17x - 15 = 0

Complex Numbers (How to find the nth root)
Example:
Solve x⁴ + 8√3 + 8i = 0

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