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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 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:

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

**Complex Numbers: Roots of a cubic equation**

Examples:

- Find all the roots of the equation x
^{3}- 4x^{2}+ x + 26 = 0 - Find all the roots of the equation x
^{3}- 7x^{2}+ 17x - 15 = 0

**Complex Numbers (How to find the nth root)**

Example:

Solve x^{4} + 8√3 + 8i = 0

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