The Complex Exponential

t

-5

Re(λ)

0

Im(λ)

3.1412

viewpoint

above

front

right

Argand plane

box and axes

z

(0.+3.1412)t



This Demonstration plots the complex exponential

z=

λt



. In the starting orientation ("above"),

t

increases from -5 on the left to 5 on the right. You are looking down on the Argand plane along the positive imaginary axis—turn on the "Argand plane" checkbox to see it. (Note: animations may be jerky with this option on.) The real and imaginary parts of

λ

are controlled by the real and imaginary sliders. In the starting position,

λ=π

, and the plot is a left-handed helix. The

t

slider controls the position of the gray ball.