IB DP Maths: AI HL复习笔记1.5.1 Intro to Complex Numbers-翰林国际教育

IB DP Maths: AI HL复习笔记1.5.1 Intro to Complex Numbers

Complex numbers are a set of numbers which contain both a real part, and an imaginary part.

Remember that complex numbers have both a real part and an imaginary part
- 1 is purely real (its imaginary part is zero)
- i is purely imaginary (its real part is zero)
- 1 + i is a complex number (both the real and imaginary parts are equal to 1)

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Adding and subtracting complex numbers should be done when they are in Cartesian form
When adding and subtracting complex numbers, simplify the real and imaginary parts separately
- Just like you would when collecting like terms in algebra and surds, or dealing with different components in vectorsHow do I multiply complex numbers in Cartesian Form?

When revising for your exams, practice using your GDC to check any calculations you do with complex numbers by hand
- This will speed up using your GDC in rectangular form whilst also giving you lots of practice of carrying out calculations by hand

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When dividing complex numbers, the complex conjugate is used to change the denominator to a real number.

To divide two complex numbers:
- STEP 1: Express the calculation in the form of a fraction
- STEP 2: Multiply the top and bottom by the conjugate of the denominator:
  - This ensures we are multiplying by 1; so not affecting the overall value
- STEP 3: Multiply out and simplify your answer
  - This should have a real number as the denominator
- STEP 4: Write your answer in Cartesian form as two terms, simplifying each term if needed
  - OR convert into the required form if needed
Your GDC will be able to divide two complex numbers in Cartesian form
- Practise doing this and use it to check your answers if you can