Complex Exponential

Select a complex number \(z = a + bi\) using the cursor and mousekey on the left graphing window. The selected number is indicated by a cyan disk. Zero is indicated by a red disk, and a straight line through \(0\) and \(z\) is drawn in yellow. This number can also be selected by grabbing the \([a]\) and \([b]\) sliders below. When the \([a]\) slider is selected, a blue line appears indicating the line along which \(z\) moves as \(a\) varies. When the \([b]\) slider is selected, a blue line appears indicating the line along which \(z\) moves as \(b\) varies.

On the right graphing plane the image of the left hand plane under the exponential map is drawn, with the red, cyan, yellow, and blue, corresponding to the features drawn on the left plane.

Grab the \([t]\) slider to cause \(z\) to move from \(0\) to \(a + bi\) while \(e^z\) moves along a spiral from \(1\) to \(e^{a+bi}\).