Mathematics, 23.07.2019 07:40 kodak0531
The complex number z = –1 + 3i can be expressed in trigonometric form as:
Answers: 1
![\bf z=\stackrel{a}{-1}\stackrel{b}{+3}i\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad \qquad z=r[cos(\theta )i~sin(\theta )]\\\\ -------------------------------\\\\ r=\sqrt{(-1)^2+3^2}\implies r=\sqrt{10} \\\\\\ \theta =tan^{-1}\left( \frac{3}{-1} \right)\implies \theta \approx -71.57\implies \theta \approx\stackrel{360-71.57}{288.43^o}\\\\ -------------------------------\\\\ z=\sqrt{10}\left[ cos(288.43^o)+i~sin(288.43^o) \right]](/tpl/images/0122/6556/59e8c.png)
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The complex number z = –1 + 3i can be expressed in trigonometric form as:...
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