# Simple Motion Made Complex

**Calculus**Level 3

As an object moves in a plane let its position be represented by the complex function

\[ \large z(t) = A \, e^{i \omega t} \]

where A is a positive number, \( \omega \) is a real number, and \( t\) is a real variable representing time.

What type of motion does the object have?

**Note**: There are six choices. If necessary scroll down to see them.

**Hint**: Here the \(xy\)-plane has been replaced with the complex plane. \(z \) is **NOT** the Cartesian co-ordinate. This is motion within a plane. The number \(z\) can be thought of as the displacement of the object from the number zero.