男人资源站-涩涩五月天-加勒比一区二区-欧美丰满少妇-清纯唯美亚洲-蜜臀久久99精品久久久久宅男-1024手机在线观看-a免费在线观看-日韩一区二区三免费高清在线观看-激情欧美一区二区-日韩综合网站-色小说av-夜夜夜操操操-色片在线播放-免费在线观看中文字幕

  • 翰林提供學術活動、國際課程、科研項目一站式留學背景提升服務！
Home » 國際課程 » IB課程 » Details

IB DP Maths: AI HL復習筆記1.6.2 Forms of Complex Numbers

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月20日 上午10:42

Modulus-Argument (Polar) Form

How do I write a complex number in modulus-argument (polar) form?

  • How do I multiply complex numbers in modulus-argument (polar) form?
  • The main benefit of writing complex numbers in modulus-argument (polar) form is that they multiply and divide very easily
  • How do I divide complex numbers in modulus-argument (polar) form?
  • To?divide?two complex numbers in modulus-argument (polar) form, we?divide their moduli?and?subtract their arguments

Exam Tip

  • Worked Example

1-9-2-ib-aa-hl-forms-of-cn-we-solution-1-a

1-9-2-ib-aa-hl-forms-of-cn-we-solution-1-b

Exponential (Euler's) Form

How do we write a complex number in Euler's (exponential) form?

How do we multiply and divide complex numbers in Euler's form?

What are some common numbers in exponential form?

Exam Tip

  • Euler's form allows for easy manipulation of complex numbers, in an exam it is often worth the time converting a complex number into Euler's form if further calculations need to be carried out
    • Familiarise yourself with which calculations are easier in which form, for example multiplication and division are easiest in Euler's form but adding and subtracting are easiest in Cartesian form

Worked Example

1-9-2-ib-aa-hl-forms-of-cn-we-solution-2-eulers

Conversion of Forms

Converting from Cartesian form to modulus-argument (polar) form or exponential (Euler's) form.

  • To convert from Cartesian form to modulus-argument (polar) form or exponential (Euler) form use

Converting from modulus-argument (polar) form or exponential (Euler's) form to Cartesian form.

  • To convert from modulus-argument (polar) form to Cartesian form
    • Write?z?=?r?(cosθ+ isinθ)as?z?=?r?cosθ+ (r?sinθ?)i
    • Find the values of the trigonometric ratios?r?sinθand?r?cosθ
      • You may need to use your knowledge of trig exact values
    • Rewrite as?z = a + bi where
      • a = r?cosθ and?b?=?r?sinθ
  • To convert from exponential (Euler’s) form to Cartesian form first rewrite?z?=?r?eiθin the form?z?=?r?cosθ+ (r?sinθ)i and then follow the steps above

Exam Tip

  • When converting from Cartesian form into Polar or Euler's form, always leave your modulus and argument as an exact value
    • Rounding values too early may result in inaccuracies later on

Worked Example

1-9-2-ib-aa-hl-forms-of-cn-we-solution-3-a

1-9-2-ib-aa-hl-forms-of-cn-we-solution-3-b

 

 

 

 

轉載自savemyexams

? 2025. All Rights Reserved. 滬ICP備2023009024號-1

國際競賽 國際競賽
了解背提項目
國際課程 國際課程
國際課程
商務合作 商務合作
商務合作
課程試聽 課程試聽