Moduli of Complex Numbers (Grades 11-12)

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Moduli of Complex Numbers

1. 
What is the modulus of [math]-4 + 7i ?[/math]
  1. [math]65[/math]
  2. [math]sqrt(65)[/math]
  3. [math]33[/math]
  4. [math]-3[/math]
2. 
Given [math]z = 8 - 2i[/math], find [math]|z|[/math].
  1. [math]2 sqrt(17)[/math]
  2. [math]2 sqrt(15)[/math]
  3. [math]68[/math]
  4. [math]60[/math]
3. 
Find the modulus of [math]-3i[/math].
  1. [math]-3[/math]
  2. [math]sqrt(3)[/math]
  3. [math]sqrt(-3)[/math]
  4. [math]3[/math]
4. 
If [math]z[/math] is a complex number, and [math]|z| = 5[/math], which of the following are possible values of [math]z ?[/math] Choose all correct answers.
  1. [math]z = 4 + i[/math]
  2. [math]z = 3 - 4i[/math]
  3. [math]z = 10 - 5i[/math]
  4. [math]z = 4 + 3i[/math]
5. 
Which of the following are possible values of [math]z[/math], a complex number, if [math]|z| = sqrt(13) ? [/math] Choose all correct answers.
  1. [math]z = 2 - 3i[/math]
  2. [math]z = -3 - 2i[/math]
  3. [math]z = 2 + 3i[/math]
  4. [math]z = 2sqrt(3) + i[/math]
6. 
For [math]z in CC[/math], prove that [math]|z|^2 = z bar{z}[/math].









7. 
For [math]z in CC[/math], prove that [math]|z| = | -z|[/math].









8. 
For [math]z in CC[/math], prove that [math]|z| = o <=> z = 0[/math].









9. 
For [math]z_1, z_2 in CC[/math], prove that [math]|z_1 z_2| = |z_1| |z_2| [/math].









10. 
For [math]z_1, z_2 in CC[/math] and [math]z_2!=0[/math], prove that [math]|z_1/z_2| = |z_1| / |z_2|[/math].









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