Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.4 - Roots of a Complex Number - 8.4 Problem Set - Page 447: 16

Answer

See explanation.

Work Step by Step

\begin{array}{l} 2=25=\left(60 \times 0^{\circ}+17 \sin 0^{\circ}\right) 25\\ \text { We know, } \left(\cos 360^{\circ}+15 \sin 360^{\circ}\right) 25\\ \sqrt{12}\left(\cos \frac{0}{2}+i \sin \frac{\theta}{2}\right)=z^{1 / 2} \\ =\left(\cos \frac{0^{\circ}}{2}+\hat{i} \sin \frac{0^{\circ}}{2}\right)25^{1 / 2} \end{array} \begin{array}{l} =\left(\cos \frac{360^{\circ}}{2}+i \sin \frac{360^{\circ}}{2}\right)25^{1 / 2} \\ =\left(\cos 0^{\circ}+\pi \sin 0^{\circ}\right)5 \\ \left(\cos 180^{\circ}+i \sin 180^{\circ}\right)5 \\ =5(1) \operatorname{arcs}(-1) \\ =50 \alpha-5 \\ -5 \text { or }5=z^{\prime \prime} \end{array}
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