Complex Numbers

FP1 Complex Numbers (Edexcel Further Pure Maths)
Basics - video on powers of i

Complex Numbers: Addition, Subtraction and Multiplication
Example:
z₁ = 3 + 2i
z₂ = 4 - 3i
Find:

1. z₁ + z₂
   
2. z₁ - z₂
   
3. 5z₁
   
4. i²
   
5. z₁z₂
   Expand the following:
   
6. i³
   
7. i⁴
   
8. 2i⁸ - (3i)²
   
9. (3 - 2i)⁴

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FP1 Edexcel January 2013 Q2
Example:
z = 50/(3 + 4i)
Find in the form ai + b where a,b ∈ ℝ,
(a) z
(b) z²
Find
(c) |z|
(d) arg z², giving your answer in degrees to 1 decimal place.

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