|2(a-iy)+i|=4

解

∣ 2 (a - i y) + i ∣ = 4

y = x + \frac{- 2 a + - 4 x ^{2} + 4 x + 15}{2} i, y = x - \frac{2 a + - 4 x ^{2} + 4 x + 15}{2} i; x \in R

解答ステップ

∣ 2 (a - i y) + i ∣ = 4

代用

y = x + v i

∣ 2 (a - i (x + v i)) + i ∣ = 4

拡張

∣ 2 (a - i (x + v i)) + i ∣ : 4 a^{2} + 8 a v + 4 v^{2} + 4 x^{2} - 4 x + 1

4 a^{2} + 8 a v + 4 v^{2} + 4 x^{2} - 4 x + 1 = 4

以下を解く:

v : v = \frac{- 2 a + - 4 x ^{2} + 4 x + 15}{2}, v = - \frac{2 a + - 4 x ^{2} + 4 x + 15}{2}

代用を戻す

y = x + v i

y = x + \frac{- 2 a + - 4 x ^{2} + 4 x + 15}{2} i, y = x - \frac{2 a + - 4 x ^{2} + 4 x + 15}{2} i; x \in R