Complex Numbers and Quadratic Equations

Topics in this chapter

• Complex Number Operations
• Modulus and Polar Form
• Complex Powers and Roots
• De Moivre and Roots of Unity
• Quadratic Equations and Discriminant
• Vieta Relations and Symmetric Expressions

Cheat sheet

Practice questions

1. Question 1Q-CCB8E0

   If z = 3 - 4i, where i² = -1, then the modulus of z is

   1. A.1
   2. B.5
   3. C.7
   4. D.25
   See the answer and solution
2. Question 2Q-6DEDE7

   The roots of the quadratic equation x² + 4x + 13 = 0 are

   1. A.2 ± 3i
   2. B.-2 ± 3i
   3. C.-4 ± 3i
   4. D.2 ± 13i
   See the answer and solution
3. Question 3Q-2330B3

   The value of (1 + i)/(1 - i), where i² = -1, is

   1. A.-1
   2. B.1
   3. C.i
   4. D.-i
   See the answer and solution
4. Question 4Q-3ECBBD

   Find the square roots of the complex number -7 + 24i.

   See the answer and solution
5. Question 5Q-FBA39F

   If z = 2 - 3i, where i² = -1, then z multiplied by its conjugate is

   1. A.5
   2. B.13
   3. C.-13
   4. D.4
   See the answer and solution