i(p)=3500-24p^2

解

i (p) = 3500 - 24 p^{2}

p = \frac{335999}{48} - \frac{1}{48} i, p = - \frac{335999}{48} - \frac{1}{48} i

解答ステップ

i (p) = 3500 - 24 p^{2}

代用

p = x + y i

i (x + y i) = 3500 - 24 (x + y i)^{2}

拡張

- y + i x = (3500 - 24 x^{2} + 24 y^{2}) - 48 i x y

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[- y = 3500 - 24 x^{2} + 24 y^{2} x = - 48 x y]

[- y = 3500 - 24 x^{2} + 24 y^{2} x = - 48 x y] : (x = \frac{335999}{48}, x = - \frac{335999}{48}, y = - \frac{1}{48} y = - \frac{1}{48})

代用を戻す

p = x + y i

p = \frac{335999}{48} - \frac{1}{48} i, p = - \frac{335999}{48} - \frac{1}{48} i