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Bentuk polar dari $$$15625 + \frac{719413999 i}{1000000000}$$$
Masukan Anda
Temukan bentuk polar dari $$$15625 + \frac{719413999 i}{1000000000}$$$.
Solusi
Bentuk standar dari bilangan kompleks tersebut adalah $$$15625 + \frac{719413999 i}{1000000000}$$$.
Untuk suatu bilangan kompleks $$$a + b i$$$, bentuk kutub diberikan oleh $$$r \left(\cos{\left(\theta \right)} + i \sin{\left(\theta \right)}\right)$$$, di mana $$$r = \sqrt{a^{2} + b^{2}}$$$ dan $$$\theta = \operatorname{atan}{\left(\frac{b}{a} \right)}$$$.
Kita peroleh bahwa $$$a = 15625$$$ dan $$$b = \frac{719413999}{1000000000}$$$.
Dengan demikian, $$$r = \sqrt{15625^{2} + \left(\frac{719413999}{1000000000}\right)^{2}} = \frac{\sqrt{244140625517556501957172001}}{1000000000}.$$$
Selain itu, $$$\theta = \operatorname{atan}{\left(\frac{\frac{719413999}{1000000000}}{15625} \right)} = \operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)}.$$$
Oleh karena itu, $$$15625 + \frac{719413999 i}{1000000000} = \frac{\sqrt{244140625517556501957172001}}{1000000000} \left(\cos{\left(\operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)} \right)} + i \sin{\left(\operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)} \right)}\right).$$$
Jawaban
$$$15625 + \frac{719413999 i}{1000000000} = \frac{\sqrt{244140625517556501957172001}}{1000000000} \left(\cos{\left(\operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)} \right)} + i \sin{\left(\operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)} \right)}\right) = \frac{\sqrt{244140625517556501957172001}}{1000000000} \left(\cos{\left(\left(\frac{180 \operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)}}{\pi}\right)^{\circ} \right)} + i \sin{\left(\left(\frac{180 \operatorname{atan}{\left(\frac{719413999}{15625000000000} \right)}}{\pi}\right)^{\circ} \right)}\right)$$$A