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受欢迎的代数 >

aa-2a-3i=0

解答

aa - 2 a - 3 i = 0

解答

a = - 0.44261 \dots - 1.03977 \dots i, a = 2.44261 \dots + 1.03977 \dots i

求解步骤

aa - 2 a - 3 i = 0

替代

a = x + y i

(x + y i) (x + y i) - 2 (x + y i) - 3 i = 0

展开

(x + y i) (x + y i) - 2 (x + y i) - 3 i : (x^{2} - y^{2} - 2 x) + i (- 3 - 2 y + 2 x y)

(x^{2} - y^{2} - 2 x) + i (- 3 - 2 y + 2 x y) = 0

将

0

改写成标准复数形式:

0 + 0 i

(x^{2} - y^{2} - 2 x) + i (- 3 - 2 y + 2 x y) = 0 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[x^{2} - y^{2} - 2 x = 0 - 3 - 2 y + 2 x y = 0]

[x^{2} - y^{2} - 2 x = 0 - 3 - 2 y + 2 x y = 0] : (x = - 0.44261 \dots, x = 2.44261 \dots, y = - 1.03977 \dots y = 1.03977 \dots)

a = x + y i

代回

a = - 0.44261 \dots - 1.03977 \dots i, a = 2.44261 \dots + 1.03977 \dots i

流行的例子

x - y i = - 2 + 3 i

\frac{1}{2 - i} = a + ib

(x+yi)(2-3i)=4+i

(x + y i) (2 - 3 i) = 4 + i

(3+2i)(2-3i)-(1+2i)(2-i)=m+ni

(3 + 2 i) (2 - 3 i) - (1 + 2 i) (2 - i) = m + ni

∣ z - 5 - 6 i ∣ = 4