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首頁(yè) » 生活常識(shí) » 求輻角主值的方法(怎么求幅角的主值)

求輻角主值的方法(怎么求幅角的主值)

分類：生活常識(shí) 日期：2022-07-28 05:20 瀏覽：9 次

1.怎么求幅角的主值

任意一個(gè)復(fù)數(shù)z=a+bi(a、b∈R)都與復(fù)平面內(nèi)以原點(diǎn)O為始點(diǎn)，復(fù)數(shù)z在復(fù)平面內(nèi)的對(duì)應(yīng)點(diǎn)Z為終點(diǎn)的向量一一對(duì)應(yīng)。復(fù)數(shù)的輻角是以x軸的正半軸為始邊，向量OZ所在的射線（起點(diǎn)是O）為終邊的角θ。

輻角主值的范圍是-π&lt；θ&lt；=π。求法其實(shí)很簡(jiǎn)單，就是求一個(gè)反正切的值。θ=arctgb/a.

a>0,b>o在第一象限，這個(gè)象限內(nèi)幅角為（0，π/2）

a<0,b>0，在第二象限 （π/2，π）

a<0.b<0，在第三象限 （-π/2，-π）

a>0,b<0，在第四象限 （0，-π/2）

2.復(fù)數(shù)的三角形式,我不會(huì)求輻角主值,求過(guò)程解決方式

非零復(fù)數(shù)Z=a+bi的輻角是以x軸的正半軸為始邊，以復(fù)數(shù)的向量OZ所在的射線（起點(diǎn)是O）為終邊的角θ。Z的輻角有無(wú)限多個(gè)值，且這些值相差2π的整數(shù)倍。把適合于-π&lt；θ&lt；=π的輻角θ 的值叫做輻角主值，其值是唯一的。

用三角函數(shù)表示：非零復(fù)數(shù)Z=a+bi的輻角θ=arctan(b/a)，（ θ 在Z所在象限）

例子：求復(fù)數(shù)Z=4-4i的輻角主值。

解：已知復(fù)數(shù)Z的實(shí)部a=4，虛部b=-4，所以Z在第四象限，

其輻角 θ= arctan(b/a)=arctan(-1)=（-π/4）+ 2kπ，（k

為實(shí)數(shù)）

因?yàn)?π&lt；-π/4&lt； π，所以- π/4是復(fù)數(shù)Z的輻角主值。

（注：tan θ=b/a=-1， θ=（3π/4）+2kπ在第二象限，舍去）

學(xué)得向量，也可以用向量法求得：

A=1+0i，向量OA=(1,0),OZ=(a,b)

|OA|=1,|OZ|^2=a^2+b^2,

OA·OZ=(1,0)·（a,b）=a

由公式OA·OZ=|OA|·|OZ|·cosθ求得 θ，

注意θ是兩向量的夾角，其取值0&lt；= θ&lt；=π，

根據(jù)Z所在象限判斷其輻角主值是 θ還是 θ-π 。

3.怎么求幅角的主值

任意一個(gè)復(fù)數(shù)z=a+bi(a、b∈R)都與復(fù)平面內(nèi)以原點(diǎn)O為始點(diǎn)，復(fù)數(shù)z在復(fù)平面內(nèi)的對(duì)應(yīng)點(diǎn)Z為終點(diǎn)的向量一一對(duì)應(yīng)。

復(fù)數(shù)的輻角是以x軸的正半軸為始邊，向量OZ所在的射線（起點(diǎn)是O）為終邊的角θ。輻角主值的范圍是-π<θ<=π。

求法其實(shí)很簡(jiǎn)單，就是求一個(gè)反正切的值。θ=arctgb/a.a>0,b>o在第一象限，這個(gè)象限內(nèi)幅角為（0，π/2）a0，在第二象限 （π/2，π）a<0.b0,b<0，在第四象限 （0，-π/2）。

4.復(fù)變函數(shù) 輻角主值 計(jì)算公式

z=-2=2(cosπ+isinπ)所以，z=-2的幅角主值為π在復(fù)平面上，復(fù)數(shù)所對(duì)應(yīng)的向量與x軸正方向的夾角成為復(fù)數(shù)的輻角，顯然一個(gè)復(fù)數(shù)的輻角有無(wú)窮多個(gè)，但是在2113區(qū)間（-π，π]內(nèi)的只有一個(gè)，這個(gè)輻角就是該向量的輻角主值，也稱主輻角，記為argz。

復(fù)數(shù)的模與輻角是復(fù)數(shù)三角形式表示的兩個(gè)基本元素，復(fù)數(shù)所對(duì)應(yīng)的向量長(zhǎng)度稱為復(fù)數(shù)的幅值，該向量與實(shí)軸正方5261向的夾角為復(fù)數(shù)的輻角。輻角的大小有無(wú)窮多，但是輻角主值唯一確定。

擴(kuò)展資料：復(fù)變函數(shù)也研究多值函數(shù)，黎曼曲面理論是研究多值函數(shù)的主要工具。由許多層面安放在一起而構(gòu)成的一種曲面叫做黎曼曲面。

利用這種曲面，可以使多值函數(shù)的單值枝和枝點(diǎn)概念在幾何上有非常直觀的表示和說(shuō)明。對(duì)于某一個(gè)多值函數(shù)，如果能作出它的黎曼曲面，那么，函數(shù)在黎曼曲面上就變成單值函數(shù)。

黎曼曲面理論是復(fù)變函數(shù)域和幾何間的一座橋梁，能夠使我們把比較深?yuàn)W的函數(shù)的解析性質(zhì)和幾何聯(lián)系起來(lái)。現(xiàn)時(shí)，關(guān)于黎曼曲面的研究還對(duì)另一門(mén)數(shù)學(xué)分支拓?fù)鋵W(xué)有比較大的影響，逐漸地趨向于討論它的拓?fù)湫再|(zhì)。

參考資料來(lái)源：百度百科-復(fù)變函數(shù)。

5.輔角主值怎么找,舉例說(shuō)明一下

三角形式。復(fù)數(shù)z=a+bi化為三角形式

z=r(cosθ+sinθi)

式中r= sqrt(a^2+b^2)，是復(fù)數(shù)的模（即絕對(duì)值）；

θ 是以x軸為始邊，射線OZ為終邊的角，叫做復(fù)數(shù)的輻角，記作argz，即

argz=θ =arctan(b/a),

設(shè)z=r(cosθ+sinθi)=rcosθ+rsinθi)

如 z=1-i

在復(fù)數(shù)坐標(biāo)系中

k=b/a=(-1)/1=-1

所以輻角主值為3π/4

求輻角主值的方法有哪些

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