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## More Notation and Terminology

It’s already been mentioned that the rectilinear coordinates of a complex number in the complex plane are called the

real partandimaginary part, respectively.We also have special notation and various names for the radius and angle of a complex number expressed in polar coordinates :

The

complex conjugateof is denoted and is defined by

where, of course, . Sometimes you’ll see the notation in place of , but we won’t use that here.In general, you can always obtain the complex conjugate of any expression by simply replacing with . In the complex plane, this is a

vertical flipabout the real axis; in other words, complex conjugation replaces each point in the complex plane by itsmirror imageon the other side of the axis.