Work out complex conjugate instantly with clear inputs, formula shown and shareable results.
The conjugate flips the sign of the imaginary part, reflecting the number across the real axis. Multiplying a number by its conjugate always gives the real value |z|², which is why conjugates clear denominators.
Conjugate
conj(a + bi) = a − bi, z·z̄ = a² + b² = |z|²
7 + 24i, and their product is 49 + 576 = 625 = 25².
For real coefficients, conjugating the whole equation shows that if z is a root then so is z̄.