conjugate

The same two-term expression with the middle sign flipped — $a+b$ and $a-b$ .

The conjugate of a two-term expression $a+b$ is $a-b$ (and vice versa) — same two terms, opposite sign between them. Multiplying a radical or complex expression by its conjugate clears the radical (or the imaginary part) via the difference-of-squares pattern: $(a+b)(a-b) = a^2 - b^2$ .

Examples

The conjugate of $\sqrt{x} - 3$ is $\sqrt{x} + 3$ .
The conjugate of $2 + \sqrt5$ is $2 - \sqrt5$ ; their product is $4 - 5 = -1$ .