91Ó°ÊÓ

What is a directed line segment?

Show that the given complex number \(z\) plots as a point in the Mandelbrot set. a. Write the first six terms of the sequence \(z_{1}, z_{2}, z_{3}, z_{4}, z_{5}, z_{6}, \dots\) where \(z_{1}=z:\) Write the given number. \(z_{2}=z^{2}+z:\) Square \(z_{1}\) and add the given number. \(z_{3}=\left(z^{2}+z\right)^{2}+z:\) Square \(z_{2}\) and add the given number. \(z_{4}=\left[\left(z^{2}+z\right)^{2}+z\right]^{2}+z:\) Square \(z_{3}\) and add the given number. \(z_{5}:\) Square \(z_{4}\) and add the given number. \(z_{6}:\) Square \(z_{5}\) and add the given number. b. If the sequence that you began writing in part (a) is bounded, the given complex number belongs to the Mandelbrot set. Show that the sequence is bounded by writing two complex numbers. One complex number should be greater in absolute value than the absolute values of the terms in the sequence. The second complex number should be less in absolute value than the absolute values of the terms in the sequence. $$z=-i$$

Plot each of the complex fourth roots of 1

Solve and graph the solution set on a number line: $$|2 x+3| \leq 13$$ (Section P.9, Example 8)