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# 复数介绍

• ${i}^{2}=-1$
• $\sqrt{-1}=i$

## 复数定义

$\begin{array}{ccc}a& +& bi\\ ↑& & ↑\phantom{i}\\ \text{实数}& & \text{虚数}\\ \text{部分}& & \text{部分}\end{array}$
$a$ 叫做数字的 $\text{实数}$ 部分, $b$ 叫做数字的 $\text{虚数}$ 部分.

$7i-2$$-2+7i$实部是 $-2$ 虚部是$7$.
$4-3i$$4+\left(-3\right)i$实部是$4$ 虚部是 $-3$
$9i$$0+9i$实部 $0$ 虚部是 $9$
$2$$-2+0i$实部是$-2$ 虚部是$0$

## 检查你对内容的理解

$13.2i+1$的实部是几？

$21-14i$的虚部是几？

$17i$的实部是几？

## 复数的分类

$\overline{)\begin{array}{c}\text{复数}\\ \\ \begin{array}{lcr}4+2i& & -3-\sqrt{5}i\end{array}\\ \\ \overline{)\begin{array}{c}\text{实数}\\ \\ \begin{array}{lcr}\sqrt{5}& -12.2& 3\end{array}\end{array}}\\ \\ \overline{)\begin{array}{c}\text{虚数}\\ \\ \begin{array}{lcr}\sqrt{5}i& -12.2i& 3i\end{array}\end{array}}\end{array}}$

### 例题

$\begin{array}{rl}& \text{实数}\\ & \left(b=0\right)\end{array}$$\begin{array}{rl}& \text{虚数}\\ & \left(a=0\right)\end{array}$$\begin{array}{rl}& \text{复数}\\ & \left(a+bi\right)\end{array}$
$\begin{array}{rl}& 7+8i\\ & \left(7+8i\right)\end{array}$X
$\begin{array}{rl}& \sqrt{3}\\ & \left(\sqrt{3}+0i\right)\end{array}$XX
$\begin{array}{rl}& 1\\ & \left(1+0i\right)\end{array}$XX
$\begin{array}{rl}& -1.3i\\ & \left(0+\left(-1.3\right)i\right)\end{array}$XX
$\begin{array}{rl}& 100i\\ & \left(0+100i\right)\end{array}$XX

## 练习

$-2+3i$是什么类型的数？

$10.2$是什么类型的数？

$-17i$是什么类型的数？