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Chapter 6: Problem 6
The directed line segment whose initial point is the origin is said to be in ________ ________ .
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In Exercises 67-82, use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. $$ 4(1-\sqrt{3} i)^{3} $$
In Exercises \(47-58\) , perform the operation and leave the result in trigonometric form. $$ \left[\frac{3}{4}\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)\right]\left[4\left(\cos \frac{3 \pi}{4}+i \sin \frac{3 \pi}{4}\right)\right] $$
THINK ABOUT IT What can be said about the vectors \(\mathbf{u}\) and \(\mathbf{v}\) under each condition? (a) The projection of \(\mathbf{u}\) onto \(\mathbf{v}\) equals \(\mathbf{u}\). (b) The projection of \(\mathbf{u}\) onto \(\mathbf{v}\) equals \(\mathbf{0}\).
TRUE OR FALSE? In Exercises 107 and 108, determine whether the statement is true or false. Justify your answer. Geometrically, the \(n\)th roots of any complex number \(z\) are all equally spaced around the unit circle centered at the origin.
In Exercises 67-82, use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. \([3(\cos\ 15^{\circ}\ +\ i\ \sin\ 15^{\circ}]^4\)
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