Question

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

Answer 1

Answer:

This is an ellipse.

Step-by-step 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.