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%% Plot of Complex Base 10 Logarithm % %% % Define a grid of values for the (X,Y) domain. % Copyright 2015 The MathWorks, Inc. [X,Y] = meshgrid(-5:0.25:5,-5:0.25:5); %% % Calculate the complex base 10 logarithm on the grid. Z = log10(X+1i*Y); %% % Make a surface plot of the imaginary portion of the function. figure surf(X,Y,imag(Z)) grid on hold on title('Principal Branch of Im[$\log_{10}(X+iY)$]','Interpreter','latex') xlabel('X') ylabel('Y') zlabel('Z') view(44,42) %% % On the complex plane, the common logarithm is a multivalued function % that winds around the origin. %% % Since % % $$\log_{10}(X) = \frac{\log(X)}{\log(10)},$$ % % you can obtain another branch of the function by adding $2 \pi i/ % \log(10)$ to the |Z| values. z2 = Z + 2*pi*1i/log(10); surf(X,Y,imag(z2)) title('Two Branches of the Complex Base 10 Logarithm') view(45,22) hold off %% % In this plot, the branches are stacked on top of each other and meet % along the negative real axis.