25-m^2=(-1)^2+(mi+2i)^2

解答

25 - m^{2} = (- 1)^{2} + (mi + 2 i)^{2}

m = - 7

求解步骤

25 - m^{2} = (- 1)^{2} + (mi + 2 i)^{2}

替代

m = x + y i

25 - (x + y i)^{2} = (- 1)^{2} + ((x + y i) i + 2 i)^{2}

乘开

(25 - x^{2} + y^{2}) - 2 i x y = (- x^{2} - 4 x + y^{2} - 3) + i (- 4 y - 2 x y)

复数仅在实部和虚部均相等时才相等改写为方程组:

[25 - x^{2} + y^{2} = - x^{2} - 4 x + y^{2} - 3 - 2 x y = - 4 y - 2 x y]

[25 - x^{2} + y^{2} = - x^{2} - 4 x + y^{2} - 3 - 2 x y = - 4 y - 2 x y] : (x = - 7, y = 0)

m = x + y i

代回

m = - 7

\frac{z - 5 i}{z + 2} = 4 i

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

z - (\frac{1}{z}) = 1 + 5 i

z^{2} = - (\frac{4 i}{3})

\frac{1 + i}{z} - (4 + 3 i) = i