A Level Maths Session
|Inverse Function||Exponential Function||Maclaurin Series||Complex Number Exponential Form|
Complex Number Exponential Form
Welcome to this session.
ExercisesPlease try these questions.
Given 2+3i. Treat 2 (the real part) as an x coordinate and 3 (the imaginary part) as a y coordinate.
- Sketch the x,y axes and mark this point on the graph. Label it P.
- Draw the line OP and find its length r. (Call r the “modulus”).
- Find the angle θ between OP and the x axis. (Call θ the “argument”).
- Rewrite 2+3i in the form r(cosθ + i sinθ). (Called the polar form).
Prove that cosθ + i sinθ = eiθ using these steps:
- Write out the first 4 terms in the Maclaurin’s series for cosθ, sinθ and eiθ.
- Show for the first 4 terms that cosθ + i sinθ = eiθ. (Called Euler’s formula.)
- Given 2+3i. Write this in the form r eiθ. Call this the exponential form.
Past Exam QuestionsIn this video, I shall go through some past exam questions.
Thanks for attending this session.
9 May 2014