2.3 - Complex Numbers

# 2.3 - Complex Numbers - &amp;amp;lt;?xml...

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Unformatted text preview: &lt;?xml version=&quot;1.0&quot; encoding=&quot;iso-8859-1&quot;?&gt; &lt;!DOCTYPE html PUBLIC &quot;-//W3C//DTD XHTML 1.0 Strict//EN&quot; &quot;http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd&quot;&gt; &lt;html xmlns=&quot;http://www.w3.org/1999/xhtml&quot;&gt; &lt;head&gt; &lt;title&gt;2.3 - Complex Numbers&lt;/title&gt; &lt;meta http-equiv=&quot;Content-Type&quot; content=&quot;text/html; charset=iso-8859-1&quot; /&gt; &lt;link href=&quot;../m116.css&quot; rel=&quot;stylesheet&quot; type=&quot;text/css&quot; /&gt; &lt;/head&gt; &lt;body&gt; &lt;h1&gt;2.3 - Complex Numbers&lt;/h1&gt; &lt;h2&gt;Imaginary number, i&lt;/h2&gt; &lt;p&gt;The square of no real number can be negative. That, however, leaves certain equations (like x&lt;sup&gt;2&lt;/sup&gt;+1=0) with no real solution. We mathematicians don't like things not to have an answer. So, we came up an imaginary number &lt;em&gt;i&lt;/em&gt; such that &lt;em&gt;i&lt;/em&gt;&lt;sup&gt;2&lt;/sup&gt; = -1. That makes &lt;em&gt;i&lt;/em&gt;=sqrt(-1). &lt;/p&gt; &lt;p&gt;It is important to remember that &lt;em&gt;i&lt;/em&gt; is an imaginary number. There will never be a &lt;em&gt;real&lt;/em&gt; number whose square is negative. Since we graph equations in the &lt;em&gt;real&lt;/em&gt; world, solutions that involve &lt;em&gt;i&lt;/em&gt; will not appear on the graph.&lt;/p&gt; &lt;h2&gt;Complex Numbers&lt;/h2&gt; &lt;p&gt;Every complex number can be written as &amp;quot;a + b&lt;em&gt;i&lt;/em&gt;&amp;quot; where...
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## This note was uploaded on 10/18/2011 for the course MAT 1033 taught by Professor Brown during the Spring '10 term at Valencia.

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2.3 - Complex Numbers - &amp;amp;lt;?xml...

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