Changes

Many functions used in real analysis can be extended in to complex numbers using [[Taylor series]]. This is the subject of [[complex analysis]].

Many functions used in real analysis can be extended in to complex numbers using [[Taylor series]]. This is the subject of [[complex analysis]].

It is a common belief that [[complex]] numbers have a weaker connection to physical reality than real numbers. Observables in [[Physics]] for example weight, energy, pressure etc. are usually represented as [[real]] [[numbers]], and the SI system of units relies on real numbers. However, the transformation between a SI base unit, e.g. an inductance/capacitance/resistance value and a complex impedance is arbritrary and set by convention, and the "natural" representation depends on  the measurement method. As a matter of fact, a number of measurement devices (network analysers, lock in amplifiers) directly output real and imaginary component (where the imaginary component is obviously a real voltage/current value).

It is a common belief that complex numbers have a weaker connection to physical reality than real numbers. Observables in [[Physics]] for example weight, energy, pressure etc. are usually represented as [[real]] [[numbers]], and the SI system of units relies on real numbers. However, the transformation between a SI base unit, e.g. an inductance/capacitance/resistance value and a complex impedance is arbritrary and set by convention, and the "natural" representation depends on  the measurement method. As a matter of fact, a number of measurement devices (network analysers, lock in amplifiers) directly output real and imaginary component (where the imaginary component is obviously a real voltage/current value).  Also, the [[index of refraction]] is often expressed as a complex number whose imaginary component indicates [[absorption]] loss as light propagates through the medium.

===Polar notation===

===Polar notation===