Tim Gan Math
Sign up free

Properties from Exponential or Trigonometric form Q3

Properties from Exponential or Trigonometric form Q3

The complex number \(z\) has a modulus \(r\) and principal argument \(\theta\) where \(0<\theta<\dfrac{\pi}{2}\).

Find, in terms of \(r\) and \(\theta\), the modulus and argument of

  1. \(z^{-1}\)
  2. \(z^{2}\)
  3. \(iz\)
  4. \(z z^{*}\)

Video Solution:

Video Solution

Video solution locked

A free account saves your progress; this video needs tuition enrolment.

Create free accountSign inIB Math tuition

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create free accountSign inIB Math tuition

Create a free account to practise similar questions.

Create free accountSign inIB Math tuition
Answer:(i) |z⁻¹|=1/r, arg(z⁻¹)=-θ; (ii) |z²|=r², arg(z²)=2θ; (iii) |iz|=r, arg(iz)=π/2+θ; (iv) \(|zz^*|=r^2, \arg(zz^*)=0\)

Need help? Join our JC Math tuition classes.

Learn more