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Chapter 6: Problem 5
Plot each complex number and find its absolute value. $$z=3+2 i$$
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Use a graphing utility to graph \(r=\sin n \theta\) for \(n=1,2,3,4,5\) and \(6 .\) Use a separate viewing screen for each of the six graphs. What is the pattern for the number of loops that occur corresponding to each value of \(n ?\) What is happening to the shape of the graphs as \(n\) increases? For each graph, what is the smallest interval for \(\theta\) so that the graph is traced only once?
Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=8 \mathbf{i}-4 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-12 \mathbf{j}$$
Using words and no symbols, describe how to find the \(\mathrm{d}\) product of two vectors with the alternative formula $$\mathbf{v} \cdot \mathbf{w}=\|\mathbf{v}\|\|\mathbf{w}\| \cos \theta$$
Find the angle between \(\mathbf{v}\) and \(\mathbf{w} .\) Round to the nearest tenth of a degree. $$\mathbf{v}=-2 \mathbf{i}+5 \mathbf{j}, \quad \mathbf{w}=3 \mathbf{i}+6 \mathbf{j}$$
Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=3 \mathbf{i}, \quad \mathbf{w}=-4 \mathbf{i}$$
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