Conjugate Complex Number Calculator

Input a complex number and instantly calculate its conjugate in seconds.

Find the Conjugate of Complex Number

Complex Number: a + bi
i
Result

What Is a Conjugate Complex Number?

The conjugate of a complex number is a transformation used frequently in complex number calculations. For a given complex number \( z = a + bi \), where \( a \) is the real part and \( b \) is the imaginary part, the conjugate is represented as: \( \bar{z} = a - bi \) In other words, the conjugate flips the sign of the imaginary part while keeping the real part unchanged.

Examples

Example 1: Conjugate of \( 3 + 4i \)

Solution:

The conjugate is:

\( \overline{3 + 4i} = 3 - 4i \)

Example 2: Conjugate of \( 1 - 3i \)

Solution:

The conjugate is:

\( \overline{1 - 3i} = 1 + 3i \)