The conjugate of a complex number can be very useful when you need a real component;e.g. when rationalizing to remove the imaginary part from the denominator of a fraction.

Some useful properties:

If z is a complex number and z* is its conjugate (z* is used in some applied fields, while zbar ( a z with a bar over it) is used in most math texts)

z=a+bi, z*=a-bi where a,b are real numbers and i is the square root of negative 1.

z+z* is real.

(z)(z*) is real.

(z*)*=z. (z1+z2)*=z1*+z2*.

(z1z2)*=z1*z2*.

(z^n)*=(z*)^n.

|z*|=|z|

|z|^2=zz*=z*z

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