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Chapter 7: Problem 94
How do you determine the absolute value of a complex number?
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a polar equation that failed the symmetry test with respect to \(\theta=\frac{\pi}{2},\) so my graph will not have this kind of symmetry.
Use a graphing utility to graph each butterfly curve. Experiment with the range setting, particularly \(\theta\) step, to produce a butterfly of the best possible quality. $$\begin{aligned}&r=1.5^{\sin \theta}-2.5 \cos 4 \theta+\sin ^{7} \frac{\theta}{15} \quad \text { (Use } \quad \theta \min =0 \quad \text { and }\\\&\theta \max =20 \pi .)\end{aligned}$$
In Exercises \(81-86,\) solve equation in the complex number system. Express solutions in polar and rectangular form. $$ x^{3}-(1-i \sqrt{3})=0 $$
Exercises \(116-118\) will help you prepare for the material covered in the next section. Use the distance formula to determine if the line segment with endpoints \((-3,-3)\) and \((0,3)\) has the same length as the line segment with endpoints \((0,0)\) and \((3,6)\)
Plot each of the complex fourth roots of 1
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