In the Polar form, why is there a 2kpi? (1 Viewer)

[Vipul_K]

I was trying to comprehend the roots of a complex number. i understood demovier's theorem but I am unable to link it to the roots of complex numbers, The only part I do not understand conceptually is why is there a +2kpi?... can someone explain with reference to polar form only? (please don't use euler's form)

 

[tito981]

I was trying to comprehend the roots of a complex number. i understood demovier's theorem but I am unable to link it to the roots of complex numbers, The only part I do not understand conceptually is why is there a +2kpi?... can someone explain with reference to polar form only? (please don't use euler's form)

If you think of a sine or cos graph, the graph repeats every 2 pi because it has a period of 2pi, hence since a complex number can be expressed as z=cosx++isinx, the value of z should be the same every 2pi, as it is made up of components with period 2pi. Hence, since z is the sane for multiple 2pi's it is expressed as +2kpi.

 

[Vipul_K]

If you think of a sine or cos graph, the graph repeats every 2 pi because it has a period of 2pi, hence since a complex number can be expressed as z=cosx++isinx, the value of z should be the same every 2pi, as it is made up of components with period 2pi. Hence, since z is the sane for multiple 2pi's it is expressed as +2kpi.

OMG U ARE A LIFE SAVER.... Now I understand why.... THANKS A LOT!

 

[CM_Tutor]

I can add any integer multiple of to a complex number and get the same complex number. So,



and



because, for each of these forms, we have:



and



and



and