7.7 The exponential form - Mathematics resources

exponential formIntroductionIn addition to the cartesian and polar forms of a complex number there is a third form in whicha complex number may be written - theexponential form . In this leaflet we explain this Euler s relationsTwo important results in complex number theory are known asEuler s relations. These linkthe exponential function and the trigonometric state:Euler s relations:ej = cos +jsin ,e j = cos jsin The derivation of these relations is beyond the scope of thisleaflet. By firstly adding, and thensubtracting, Euler s relations we can obtain expressions for the trigonometric functions in termsof exponential functions. Try this!cos =ej + e j 2,sin =ej e j 2j2. The exponential form of a complex numberUsing the polar form , a complex number with modulusrand argument may be writtenz=r(cos +jsin )It follows immediately from Euler s relations that we can also write this complex number inexponential formasz=rej.

7.7 The exponential form Introduction In addition to the cartesian and polar forms of a complex number there is a third form in which a complex number may be written - the exponential form.

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  Form, Number, Complex, Exponential, The exponential form, Complex number

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