solvefor x,sif=x^2-y^2

解

解く

x, s i f = x^{2} - y^{2}

x = \frac{s f}{2 - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2}} + - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2} i, x = - \frac{s f}{2 - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2}} - - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2} i, x = \frac{s f}{2 - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}} + - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2} i, x = - \frac{s f}{2 - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}} - - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2} i

解答ステップ

s i f = x^{2} - y^{2}

代用

x = a + bi

s i f = (a + bi)^{2} - y^{2}

拡張

(a + bi)^{2} - y^{2} : (a^{2} - b^{2} - y^{2}) + 2 iab

s i f = (a^{2} - b^{2} - y^{2}) + 2 iab

標準的な複素数形式で

s i f

を書き換える:

0 + s f i

0 + s f i = (a^{2} - b^{2} - y^{2}) + 2 iab

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:

[0 = a^{2} - b^{2} - y^{2} s f = 2 ab]

[0 = a^{2} - b^{2} - y^{2} s f = 2 ab] : a = \frac{s f}{2 - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2}}, a = - \frac{s f}{2 - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2}}, a = \frac{s f}{2 - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}}, a = - \frac{s f}{2 - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}}, b = - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2} b = - - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2} b = - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2} b = - - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}

代用を戻す

x = a + bi

x = \frac{s f}{2 - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2}} + - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2} i, x = - \frac{s f}{2 - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2}} - - \frac{y ^{2} + s ^{2} f ^{2} + y ^{4}}{2} i, x = \frac{s f}{2 - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}} + - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2} i, x = - \frac{s f}{2 - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2}} - - \frac{y ^{2} - s ^{2} f ^{2} + y ^{4}}{2} i