1. Definition
The conjugate of z=a+bi is z̄=a−bi (flip the imaginary sign); z+z̄=2a and z z̄=a²+b².
3. Properties & Laws
- Imaginary sign flips;
- Sum 2a (real);
- Product a²+b²=|z|²;
- Mirror across the real axis.
4. Steps
- Enter a,b;
- Click "Conjugate";
- Or click "Load Example".
5. Worked Examples
Example: 3+4i: conjugate 3−4i, product 25.
6. Common Pitfalls
Only imaginary flips;
Product a²+b²;
Real number is its own conjugate.