Luvun $$$- \frac{5228171817}{100000000} - i$$$ napamuoto

Määritä luvun $$$- \frac{5228171817}{100000000} - i$$$ napamuoto.

Kompleksiluvun binomimuoto on $$$- \frac{5228171817}{100000000} - i$$$.

Kompleksiluvun $$$a + b i$$$ polaarimuoto annetaan muodossa $$$r \left(\cos{\left(\theta \right)} + i \sin{\left(\theta \right)}\right)$$$, missä $$$r = \sqrt{a^{2} + b^{2}}$$$ ja $$$\theta = \operatorname{atan}{\left(\frac{b}{a} \right)}$$$.

Saamme, että $$$a = - \frac{5228171817}{100000000}$$$ ja $$$b = -1$$$.

Näin ollen, $$$r = \sqrt{\left(- \frac{5228171817}{100000000}\right)^{2} + \left(-1\right)^{2}} = \frac{\sqrt{27343780548073081489}}{100000000}.$$$

Lisäksi $$$\theta = \operatorname{atan}{\left(\frac{-1}{- \frac{5228171817}{100000000}} \right)} - \pi = - \pi + \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)}.$$$

Siispä $$$- \frac{5228171817}{100000000} - i = \frac{\sqrt{27343780548073081489}}{100000000} \left(\cos{\left(- \pi + \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)} \right)} + i \sin{\left(- \pi + \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)} \right)}\right).$$$

$$$- \frac{5228171817}{100000000} - i = \frac{\sqrt{27343780548073081489}}{100000000} \left(\cos{\left(- \pi + \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)} \right)} + i \sin{\left(- \pi + \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)} \right)}\right) = \frac{\sqrt{27343780548073081489}}{100000000} \left(\cos{\left(\left(\frac{- 180 \pi + 180 \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)}}{\pi}\right)^{\circ} \right)} + i \sin{\left(\left(\frac{- 180 \pi + 180 \operatorname{atan}{\left(\frac{100000000}{5228171817} \right)}}{\pi}\right)^{\circ} \right)}\right)$$$A