Complex conjugates are two complex numbers of the form a + bi and a - bi where a and b are real numbers. Complex conjugates are denoted using a bar over the variable: If z = a + bi then z = a - bi Complex conjugates have the property that, when added together, the result is a real number.
Complex conjugates also have the property that, when multiplied together, the result is a real number.
Complex conjugates are usually used when dividing complex numbers.
|(z + w) = z + w||The conjugate of a sum is equal to the sum of the conjugates.|
|(z - w) = z - w||The conjugate of a difference is equal to the difference of the conjugates.|
|(z · w) = z · w||The conjugate of a|
|(z / w) = z / w|
||z| = |z|||The magnitude of a complex number is the same as the magnitude of its complement.|
||z2| = z·z = z·z||The magnitude of the square of a complex number equals the complex number multiplied by its conjugate.|
|The conjugate of the conjugate of a complex number equals the original complex number.|
|ez = (ez)||Euler's number (e) raised to the conjugate of a complex number is equal to the conjugate of Euler's number raised to the complex number.|
|Table 1 - Properties of complex conjugates|
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