Question

Consider the set of points defined by z = 5 cos(theta) + 3i sin(theta).

i. Plot z for theta = 0°, 90°, 180°, 270°, 360°. Based on your plot, form a conjecture about the graph of the
set of complex numbers.

Answer 1

This is an ellipse.

Explanation:

`z=5cos(\theta)+3isin(\theta)`

Applying the angle values in intervals of right angles (90°), the resulting set of values for z are:

`\theta = 0,90,180,270,360`

`z=5,3i,-5,-3i,5` (again)

If you look at the plot, you will observe how these values represent points in the xy plain. All of them belong to either the x or the y axis.

The resulting figure for the whole set of values of
`\theta` is in fact an ellipse.