(a+bi)^2=15+8i

解

(a + bi)^{2} = 15 + 8 i

(a = 4, a = - 4, b = 1 b = - 1)

解答ステップ

(a + bi)^{2} = 15 + 8 i

拡張

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

(a^{2} - b^{2}) + 2 iab = 15 + 8 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} = 15 2 ab = 8]

[a^{2} - b^{2} = 15 2 ab = 8] : (a = 4, a = - 4, b = 1 b = - 1)

(a = 4, a = - 4, b = 1 b = - 1)