1984 AMC 12 第 10 题

Question

四个复数位于复平面上一个正方形的四个顶点。其中三个数为

1+2i

、

-2+i

、

-1-2i

。第四个数为

Four complex numbers lie at the vertices of a square in the complex plane. Three of the numbers are

1+2i,

-2+i

and

-1-2i.

The fourth number is

2+i

2-i

1-2i

-1+2i

-2-i

所列顶点中有两个互为相反数

Two of the listed vertices are opposites

它们的中点是正方形的中心，因此将剩余的已知顶点关于该点对称

Their midpoint is the square’s center, so reflect the remaining given vertex through that point

点

1+2i

和

-1-2i

是相对的顶点，所以它们的中点

0

是正方形的中心。因此第四个顶点是

-2+i

关于原点的对称点，即

2-i

。

所以正确答案是 B。

The points

1+2i

and

-1-2i

are opposite vertices, so their midpoint

0

is the center of the square. The fourth vertex is therefore the reflection of

-2+i

through the origin, namely

2-i.

Therefore, the correct answer is B.

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