What is an imaginary number?

What is a complex number?

What is Cartesian Form?

How do I add and subtract complex numbers in Cartesian Form?

• 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?

How do I deal with higher powers of i?

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

What is a complex conjugate?

How do I divide complex numbers?

• 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