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Sine: 3D plots over the complex plane

functions.wolfram.com · 1,305 words · saved by 1 readers

in the near the real axis. Here the complex variable is expressed as . The red surface is the real part of . The blue, semitransparent surface is the imaginary part of . The pink tube is the function along the real axis. Along the real axis, the real part of is oscillating; going away from the real axis into the its absolute value is generically an exponentially increasing function. Along the real axis, the imaginary part of vanishes identically; going away from the real axis into the its absolute value is generically an exponentially increasing function. Real part over the complex plane The real part of where . The surface is colored according to the imaginary part. The right graphic is a contour plot of the scaled real part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest. Along the real axis, is oscillating; going away from the real axis into the its absolute value is generically an expon

Sine: 3D plots over the complex plane Sin Elementary Functions Sin[ z ] Visualizations 3D plots over the complex plane (31 graphics) Entering the complex plane in the near the real axis . Here the complex variable is expressed as . The red surface is the real part of . The blue, semitransparent surface is the imaginary part of . The pink tube is the function along the real axis . Along the real axis , the real part of is oscillating ; going away from the real axis into the its absolute value is generically an exponentially increasing function. Along the real axis , the imaginary part of vanish

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