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Complex Conjugate

The complex conjugate of a + bi  is abi, and similarly the complex conjugate of abi  is a + bi. This consists of changing the sign of the imaginary part of a complex number. The real part is left unchanged.

Complex conjugates are indicated using a horizontal line over the number or variable. For example, .

Note: Complex conjugates are similar to, but not the same as, conjugates.

Expression Complex Conjugate
 5 – 2i 4i + 1 –5i 12
 5 + 2i –4i + 1 5i 12

Complex number formulas