Electrical Engineering ⇒ Topic : Notation of Phasors on Rectangular Coordinate Axes

Nathan
 
Consider a phasor V lying along OXaxis as shown in Fig. (a). If we multiply this phasor by 1, the phasor is reversed i.e. it is rotated through 180° in the counterclockwise (CCW) direction. Let us see with what factor the phasor be multiplied so that it rotates through 90° in CCW direction. Suppose this factor is j. As shown in Fig. (a), multiplying the phasor by j^{2} rotates the phasor through 180° in CCW direction. This means that multiplying the phasor by j^{2} is the same as multiplying by 1. It follows, therefore, that
We anive at a very important conclusion that when a phasor is multiplied by j (= √1), the phasor is rotated through 900 in CCW direction. Each successive multiplication by j rotates the phasor through an additional 90° in CCW direction. It is easy to see that multiplying a phasor by
Fig. (a) shows the effect of multiplying a phasor by j. The following points may be noted carefully
figure (a)
 
 
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