Complex Conjugate Calculator
MathFind the complex conjugate and absolute value of a complex number.
Conjugate
The complex conjugate, formed by flipping the sign of the imaginary part.
Absolute Value |z|
2.828427
The distance from the origin to the complex number, sqrt(a^2+b^2).
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Frequently Asked Questions
What is a complex conjugate?
The conjugate of a+bi is a-bi, formed by keeping the real part the same and flipping the sign of the imaginary part.
What is the complex conjugate used for?
Multiplying a complex number by its own conjugate always produces a real number (a^2+b^2), which is exactly the technique used to divide complex numbers or clear an imaginary part from a denominator.
Why does the conjugate have the same absolute value as the original number?
Flipping the sign of the imaginary part reflects the point across the real axis, which doesn't change its distance from the origin, so |a+bi| = |a-bi| always.
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