Solutions for Polar Form of Complex Numbers
Solutions to Try Its
1.![Plot of 1+5i in the complex plane (1 along the real axis, 5 along the imaginary axis).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/923/2015/04/25181429/CNX_Precalc_Figure_08_05_0022.jpg)
Solutions to Odd-Numbered Answers
1. a is the real part, b is the imaginary part, and [latex]i=\sqrt{−1}[/latex] 3. Polar form converts the real and imaginary part of the complex number in polar form using [latex]x=r\cos\theta[/latex] and [latex]y=r\sin\theta[/latex] 5. [latex]z^{n}=r^{n}\left(\cos\left(n\theta\right)+i\sin\left(n\theta\right)\right)[/latex]. It is used to simplify polar form when a number has been raised to a power. 7. [latex]5\sqrt{2}[/latex] 9. [latex]\sqrt{38}[/latex] 11. [latex]\sqrt{14.45}[/latex] 13. [latex]4\sqrt{5}\text{cis}\left(333.4^{\circ}\right)[/latex] 15. [latex]2\text{cis}\left(\frac{\pi}{6}\right)[/latex] 17. [latex]\frac{7\sqrt{3}}{2}+i\frac{7}{2}[/latex] 19. [latex]−2\sqrt{3}−2i[/latex] 21. [latex]−1.5−i\frac{3\sqrt{3}}{2}[/latex] 23. [latex]4\sqrt{3}\text{cis}\left(198^{\circ}\right)[/latex] 25. [latex]\frac{3}{4}\text{cis}\left(180^{\circ}\right)[/latex] 27. [latex]5\sqrt{3}\text{cis}\left(\frac{17\pi}{24}\right)[/latex] 29. [latex]7\text{cis}\left(70^{\circ}\right)[/latex] 31. [latex]5\text{cis}\left(80^{\circ}\right)[/latex] 33. [latex]5\text{cis}\left(\frac{\pi}{3}\right)[/latex] 35. [latex]125\text{cis}\left(135^{\circ}\right)[/latex] 37. [latex]9\text{cis}\left(240^{\circ}\right)[/latex] 39. [latex]\text{cis}\left(\frac{3\pi}{4}\right)[/latex] 41. [latex]3\text{cis}\left(80^{\circ}\right)\text{, }3\text{cis}\left(200^{\circ}\right)\text{, }3\text{cis}\left(320^{\circ}\right)[/latex] 43. [latex]2\sqrt[3]{4}\text{cis}\left(\frac{2\pi}{9}\right)\text{, }2\sqrt[3]{4}\text{cis}\left(\frac{8\pi}{9}\right)\text{, }2\sqrt[3]{4}\text{cis}\left(\frac{14\pi}{9}\right)[/latex] 45. [latex]2\sqrt{2}\text{cis}\left(\frac{7\pi}{8}\right)\text{, }2\sqrt{2}\text{cis}\left(\frac{15\pi}{8}\right)[/latex] 47.![Plot of -3 -3i in the complex plane (-3 along real axis, -3 along imaginary axis).](http://cnx.org/resources/653589bc49c5a61087c8b5b35dea7bb550782e09/CNX_Precalc_Figure_08_05_202.jpg)
![Plot of -1 -5i in the complex plane (-1 along real axis, -5 along imaginary axis).](http://cnx.org/resources/1e202aa62de2985faf316ec1784042710afc5484/CNX_Precalc_Figure_08_05_204.jpg)
![Plot of 2i in the complex plane (0 along the real axis, 2 along the imaginary axis).](http://cnx.org/resources/3a18cb6916f29b59bb9a58a099dfa15364a877b1/CNX_Precalc_Figure_08_05_206.jpg)
![Plot of 6-2i in the complex plane (6 along the real axis, -2 along the imaginary axis).](http://cnx.org/resources/7af1e450c65a64d7f27921f8a8018bc8be30350b/CNX_Precalc_Figure_08_05_208.jpg)
![Plot of 1-4i in the complex plane (1 along the real axis, -4 along the imaginary axis).](http://cnx.org/resources/1f14632aa62a50ee4bb2768cf79779b367a439f8/CNX_Precalc_Figure_08_05_210.jpg)
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- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.