Complex conjugate
Find the conjugate of a complex number — flip the sign of the imaginary part.
z =
Complex conjugate
The conjugate of z = a + bi is z̄ = a − bi. Flip the sign of the imaginary part.
Conjugate of 3+4i is 3−4i. Conjugate of 2−7i is 2+7i.
Key property
z × z̄ = a² + b² (always real and non-negative). This equals |z|². Used to rationalize complex denominators.
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