Sunday, 22 June 2014

complex numbers - Geometrical interpretation of Im(z4)ge0



I'd like to ask you about a geometrical interpretation of the expression like Im(z4)0.




What I did:



Im [r^4(cos4α + isin4α] \ge 0



r^4sin4α ≥ 0



sin4α \ge 0



4\alpha = k \cdot \pi, k is integer




\alpha = k \cdot \frac{\pi}{4}



But how to draw it on argand diagram?
Is there any tool online? Is it possible on Wolfram Alpha?



Is it something like this?



Geometrical interpretation


Answer



Credits to Marconius.




The plot was made with Mathematica:



ContourPlot[Im[(a + I b)^4], {b, a} \[Element] Disk[], 
PlotTheme -> "Monochrome", PlotPoints -> 50,
Contours -> #] & /@ {1, 5, 10}


enter image description here


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