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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.

User Sneftel
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1 Answer

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Answer:

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.

Consider the set of points defined by z = 5 cos(theta) + 3i sin(theta). i. Plot z-example-1
Consider the set of points defined by z = 5 cos(theta) + 3i sin(theta). i. Plot z-example-2
User Peppo
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