(a+ib)^2=16+30i

解

(a + ib)^{2} = 16 + 30 i

(a = 5, a = - 5, b = 3 b = - 3)

解答ステップ

(a + ib)^{2} = 16 + 30 i

拡張

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

(a^{2} - b^{2}) + 2 iab = 16 + 30 i

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:

[a^{2} - b^{2} = 16 2 ab = 30]

[a^{2} - b^{2} = 16 2 ab = 30] : (a = 5, a = - 5, b = 3 b = - 3)

(a = 5, a = - 5, b = 3 b = - 3)