Category: 11 HL Homework

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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.

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11 HL: The Complex Modulus

Complete the following before our next class (these are from the green book).

Exercise 14A questions 3ce, 8
Exercise 14B questions 1, 5abd, 6, 8, 9, 11, 15

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11 HL: The Sine Rule

Complete the following questions before our next class.

Exercise 9A questions 1a, 3, 5, 10, 13b, 14
Exercise 9C.1 questions 1ab, 3a, 5

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11 HL: Intersecting Planes

While we’ve looked at finding the line of intersection of two planes, finding the point (or line) of intersection of three planes is actually no more difficult, so some of the questions below involve finding points (or lines) of intersection of three planes. Try to visualize the situation, and you may find GeoGebra helpful in approaching some of these questions.

Note that some of these questions instruct you to use elementary row operations (so, a matrix-based approach). I’m happy for you to use any (non-calculator) approach you like to answer these.

Exercise 13I question 1bc, 4abd, 5b, 8