Hodges Stewart
10/03/2023 · Senior High School
Given complex numbers \( z_{1} \) and \( z_{2} \) \[ z_{1}=5\left(\cos \frac{11 \pi}{4}+i \sin \frac{11 \pi}{4}\right), z_{2}=16\left(\cos \frac{11 \pi}{12}+i \sin \frac{11 \pi}{12}\right) \] Give an exact answer. Express any numbers as integers or simplified fractions. Part 1 of 2 (a) Find \( z_{1} z_{2} \) and write the product in polar form with \( 0 \leq \theta \leq 2 \pi \) The polar form is \( 80\left(\cos \frac{5 \pi}{3}+i\right. \) sin \( \left.\frac{5 \pi}{3}\right) \) Part: \( 1 / 2 \) Part 2 of 2 (b) Find \( \frac{z_{1}}{z_{2}} \) and write the quotient in polar form with \( 0 \leq \theta \leq 2 \pi \)
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The quotient \( \frac{z_{1}}{z_{2}} \) in polar form is \( \frac{5}{16} \left( \cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6} \right) \).
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