A Level Maths Session

Inverse Function Exponential Function Maclaurin Series Complex Number Exponential Form

Complex Number Exponential Form

Hi Everyone,

Welcome to this session.

proof complex number exponential form


Please try these questions.

  1. Given 2+3i. Treat 2 (the real part) as an x coordinate and 3 (the imaginary part) as a y coordinate.

    1. Sketch the x,y axes and mark this point on the graph. Label it P.
    2. Draw the line OP and find its length r. (Call r the “modulus”).
    3. Find the angle θ between OP and the x axis. (Call θ the “argument”).
    4. Rewrite 2+3i in the form r(cosθ + i sinθ). (Called the polar form).

  2. Prove that cosθ + i sinθ = e using these steps:

    1. Write out the first 4 terms in the Maclaurin’s series for cosθ, sinθ and e.
    2. Show for the first 4 terms that cosθ + i sinθ = e. (Called Euler’s formula.)

  3. Given 2+3i. Write this in the form r e. Call this the exponential form.

Past Exam Questions

In this video, I shall go through some past exam questions.

2007 H2 maths P1 Q7

Thanks for attending this session.

Dr Hock
9 May 2014