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Complex Numbers - Roots

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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 Conjugates

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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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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