x+yi=(i^3)/(2-i)

解答

x + y i = \frac{i ^{3}}{2 - i}

x = \frac{1}{5}, y = - \frac{2}{5}

求解步骤

x + y i = \frac{i ^{3}}{2 - i}

展开

\frac{i ^{3}}{2 - i} : \frac{1}{5} - \frac{2 i}{5}

x + y i = \frac{1}{5} - \frac{2 i}{5}

复数仅在实部和虚部均相等时才相等改写为方程组:

[x = \frac{1}{5} y = - \frac{2}{5}]

[x = \frac{1}{5} y = - \frac{2}{5}] : x = \frac{1}{5}, y = - \frac{2}{5}

x = \frac{1}{5}, y = - \frac{2}{5}

(3 - 2 i) (x + i y) = 2 (x - 2 i y) + 2 i - 1

(1 + i) x + (y + 5) i = 3 (1 - y)

(1 - i) x + (1 + i) y = 1 - 3 i

(x + i y)^{2} = i

(2 + 3 i) x - (1 + i) y = 3 + 4 i