11 HL: Modulus-Argument Form

Complete the following questions before our next class.

Find the modulus-argument for of the following complex numbers. Restrict your arguments to the interval \([0, 2\pi[\).

  1. 3 + 5i
  2. –3 + 5i
  3. 3 – 5i
  4. Is \(z=-2 \textrm{cis} \left(\frac{\pi}{6}\right)\) a complex number? Explain why it is not correctly expressed in modulus-argument form, and find a correct expression for \(z\) in modulus argument form.