Find the complex conjugate by keeping the real part and flipping the sign of the imaginary part.
Last updated: June 2026 | By Patchworkr Team
Enter real and imaginary parts as finite real numbers.
If z = a + bi, then its complex conjugate is z̄ = a - bi. Geometrically, this is the reflection of the point across the real axis.
Original
3 + 4i
Conjugate
3 - 4i
Original
5 - 2i
Conjugate
5 + 2i
Original
-1 + i
Conjugate
-1 - i
Original
2i
Conjugate
-2i
What happens when the imaginary part is zero?
The conjugate is the same number, because there is no imaginary sign to flip.
Does the calculator accept decimals?
Yes. It accepts finite decimals and scientific notation for both parts.
What if the input is invalid?
The calculator rejects malformed values instead of silently treating them as zero.
Why are conjugates useful?
They are used in division, polar form, and many engineering and algebraic calculations.
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