Complex number rectangular coordinates

When a system has poles that are widely different in value, it is difficult to plot them all on a root locus plot using conventional rectangular coordinates in the s plane. U is sometimes more convenient to make the root locus plots in the log s plane. Instead of using the conventional axis Re s and Im s, an ordinate of the arg s and an abscissa of the log s arc used, since the natural logarithm of a complex number is defined ... 

Solution To express equation (1.33) in rectangular coordinates, the denominator must be converted into a real, rather than complex, number. Both the numerator and the denominator are multiplied by the complex conjugate (see equations (1.23) and (1.24)). 

There are few structures known with coordination numbers larger than 8. The existence of coordination number 12 in some crystal lattices was mentioned above. Discrete nine-coordinate structures are known for complexes such as (LnlH.O) )1 and for the hydnde complexes [MHJ2- (where M = Tc or Re). These structures are formed by adding a ligand to each of the rectangular feces of a trigonal prism (Fig. 12.40). 

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