在本节和以后的小节中,大写字母表示一个点,类似的小写字母表示与它相关的复数。据/em>
虽然线在复杂几何中不如在坐标几何中漂亮,但它们仍然有一个很好的特性:据/p>
的点据span class="katex">
A.据/span>那据/span>B.据/span>那据/span>C.据/span>共线当且仅当据span class="katex">
B.据/span>−据/span>C据/span>A.据/span>−据/span>B.据/span>是真实的,或等价的,如果且仅当据/p>
A.据/span>−据/span>B.据/span>A.据/span>−据/span>B.据/span>=据/span>A.据/span>−据/span>C据/span>A.据/span>−据/span>C据/span>.据/span>
有两种类似的结果涉及线条。这是一个据A.H.R.E.F.="//www.parkandroid.com/wiki/parallel-lines/" class="wiki_link" title="平行线" target="_blank">平行线据/a>:据/p>
行据span class="katex">
A.据/span>B.据/span>和据span class="katex">
C.据/span>D.据/span>如果才是并行,只有据span class="katex">
C据/span>−据/span>D.据/span>A.据/span>−据/span>B.据/span>是真实的,或等价的,如果且仅当据/p>
A.据/span>−据/span>B.据/span>A.据/span>−据/span>B.据/span>=据/span>C据/span>−据/span>D.据/span>C据/span>−据/span>D.据/span>.据/span>
以下是结果据A.H.R.E.F.="//www.parkandroid.com/wiki/perpendicular-lines/" class="wiki_link" title="垂直的直线" target="_blank">垂直的直线据/a>:据/p>
行据span class="katex">
A.据/span>B.据/span>和据span class="katex">
C.据/span>D.据/span>是垂直的当且仅当据span class="katex">
C据/span>−据/span>D.据/span>A.据/span>−据/span>B.据/span>是纯粹的虚构,或等效,如果且仅当据/p>
A.据/span>−据/span>B.据/span>A.据/span>−据/span>B.据/span>=据/span>−据/span>C据/span>−据/span>D.据/span>C据/span>−据/span>D.据/span>.据/span>
此外,还有一个很好的表达据A.H.R.E.F.="//www.parkandroid.com/wiki/reflection/" class="wiki_link" title="反射" target="_blank">反射据/a>和复杂数字中的投影:据/p>
让据span class="katex">
W.据/span>反映据span class="katex">
Z.据/span>超过据span class="katex">
A.据/span>B.据/span>.然后据/p>
W.据/span>=据/span>A.据/span>−据/span>B.据/span>(据/span>A.据/span>−据/span>B.据/span>)据/span>Z.据/span>+据/span>A.据/span>B.据/span>−据/span>A.据/span>B.据/span>
和投影据span class="katex">
Z.据/span>到据span class="katex">
A.据/span>B.据/span>是据span class="katex">
2据/span>W.据/span>+据/span>Z.据/span>.据/p>
让据span class="katex">
m据/span>是复平面上的一条直线据/p>
(据/span>1据/span>−据/span>我据/span>)据/span>Z.据/span>+据/span>(据/span>1据/span>+据/span>我据/span>)据/span>Z.据/span>=据/span>4.据/span>.据/span>
让据span class="katex">
Z.据/span>1据/span>=据/span>2据/span>+据/span>2据/span>我据/span>是复平面上的一点。据/p>
如果反射据span class="katex">
Z.据/span>1据/span>在据span class="katex">
m据/span>是据span class="katex">
Z.据/span>2据/span>,然后计算价值据/p>
Z.据/span>1据/span>(据/span>1据/span>+据/span>我据/span>)据/span>+据/span>Z.据/span>2据/span>(据/span>1据/span>−据/span>我据/span>)据/span>.据/span>
然而,用笛卡尔坐标表示两条直线的交点是很容易的。在复坐标系中,情况并非如此:据/p>
行据span class="katex">
A.据/span>B.据/span>和据span class="katex">
C.据/span>D.据/span>相交据/p>
(据/span>A.据/span>−据/span>B.据/span>)据/span>(据/span>C据/span>−据/span>D.据/span>)据/span>−据/span>(据/span>A.据/span>−据/span>B.据/span>)据/span>(据/span>C据/span>−据/span>D.据/span>)据/span>(据/span>A.据/span>B.据/span>−据/span>A.据/span>B.据/span>)据/span>(据/span>C据/span>−据/span>D.据/span>)据/span>−据/span>(据/span>A.据/span>−据/span>B.据/span>)据/span>(据/span>C据/span>D.据/span>−据/span>C据/span>D.据/span>)据/span>那据/span>
除了几种特定情况(例如,当其中一个点为0时),这是不切实际的。据/p>