zs

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受欢迎的代数 >

|z-i|=2

解答

∣ z - i ∣ = 2

解答

z = x + (1 + - x^{2} + 4) i, z = x + (1 - - x^{2} + 4) i; x \in R

求解步骤

∣ z - i ∣ = 2

替代

z = x + y i

∣ x + y i - i ∣ = 2

展开

∣ x + y i - i ∣ : x^{2} + y^{2} - 2 y + 1

x^{2} + y^{2} - 2 y + 1 = 2

求解

y : y = 1 + - x^{2} + 4, y = 1 - - x^{2} + 4

z = x + y i

代回

z = x + (1 + - x^{2} + 4) i, z = x + (1 - - x^{2} + 4) i; x \in R

流行的例子

z^{2} = - \frac{2}{3} i

W^{2} = 3 + 4 i

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

solvefor x,x^2y+sin(y)=c

so l v e f or x, x^{2} y + sin (y) = c

z^2-(5+i)z+8+i=0

z^{2} - (5 + i) z + 8 + i = 0