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categoryرياضيات schoolبكالوريوس event_available2026-07-15

السؤال

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Sketch the effect of the complex transformation w==/5 = eLog(=)/5 =e on vertical and horizontal straight lines in the z-plane. That is, plot on the w-plane the images under w of the vertical lines z=a+it (for -5≤t≤5) with a = -4, -3, -2, -1, 0, 1, 2, 3 and 4, and the images under w of the horizontal lines z=t+ib (for -5≤t≤5) with b = -4, -3, -2, -1, 0, 1, 2, 3 and 4. [Similarly to the plot of w==/4 shown on page 91 of the Notes.]

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