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Chapter 7: Problem 46
Use Heron's Area Formula to find the area of the triangle. $$a=\frac{3}{5}, \quad b=\frac{5}{8}, \quad c=\frac{3}{8}$$
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Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$\left[5\left(\cos 140^{\circ}+i \sin 140^{\circ}\right)\right]^{3}$$
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$\left(\cos \frac{5 \pi}{4}+i \sin \frac{5 \pi}{4}\right)^{10}$$
Sketch the graph of all complex numbers \(z\) satisfying the given condition. $$|z|=5$$
Find the projection of \(\mathbf{u}\) onto \(\mathbf{v}\). Then write \(\mathbf{u}\) as the sum of two orthogonal vectors, one of which is \({\mathrm{proj}_v}\mathrm{u}.\) $$\begin{aligned} &\mathbf{u}=\langle 4,2\rangle\\\ &\mathbf{v}=\langle 1,-2\rangle \end{aligned}$$
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$\left[3\left(\cos 150^{\circ}+i \sin 150^{\circ}\right)\right]^{4}$$
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