Argument of a complex number

Determine the modulus and argument of a complex number, and denote its location on an Argand diagram... 

The phase angle of a complex number is called an argument, arg R ), and the same point may be described by the angles q> + 2m, where = 1, 2,. However, we usually need the principal value of the argument denoted by Arg R ) which is... 

At uniform rotation of a radius vector A as an argument we can take y = cot + cp. Then the real part (Re) of a complex number Z wiU change under the harmonic law ... 

This is a complex number with magnitude of one and argument equal to —ciiD. 

This example illustrates a very important property of complex numbers. The magnitude of the product of two complex numbers is the product of the magnitudes of each. The argument of the product of two complex numbers is the sum of arguments of each. 

Now, the argument (phase angle) of the product of a series of complex numbers is the sum of the arguments of the individital numbers. 

We use common (but not universal) mathematical notation and terminology for functions. When we define a function, we indicate its domain (the objects it can accept as arguments), the target space (the kind of objects it puts out as values) and a rule for calculating the value from the argument. For example, if we wish to introduce a function f that takes a complex number to its absolute value squared, we write... 

Obviously one could measure the pH of a known concentration of a weak acid and obtain a value of its hydronium ion activity, which would permit a direct evaluation of its dissociation constant. However, this would be a one-point evaluation and subject to greater errors than by titrating the acid halfway to the equivalence point. The latter approach uses a well-buffered region where the pH measurement represents the average of a large number of data points. Similar arguments can be made for the evaluation of solubility products and stability constants of complex ions. The appropriate expression for the evaluation of solubility products again is based on the half-equivalence point of the titration curve for the particular precipitation reaction [AgI(OH2)2h represents the titrant] ... 

The modulus of the complex number lei represents the amplitude Cq, while the argument Arg e represents the phase angle cat. The mathematical shorthand does not imply that strain is a complex quantity. E has the fixed values... 

---