Questions: Introduction to complex numbers
Before attempting these questions, it is highly recommended that you read Guide: Introduction to complex numbers.
Q1
Using complex numbers, find solutions to the following equations.
1.1. \(\quad x^2 = -1\)
1.2. \(\quad x^2 + 9 = 0\)
1.3. \(\quad y^2 + 160 = 16\)
1.4. \(\quad x^2 - 1 = 0\)
Q2
For each of the complex numbers below, give their real and imaginary parts. (In this question, \(a,b\) are real numbers.)
2.1. \(\quad z_1 = 2 + 3i\).
2.2. \(\quad z_2 = -23 + 32i\).
2.3. \(\quad z_3 = 3 - 3i\).
2.4. \(\quad z_4 = 3i\).
2.5. \(\quad z_5 = - 3 - 2i\).
2.6. \(\quad z_6 = a + 2bi\).
2.7. \(\quad z_7 = 2\).
2.8. \(\quad z_8 = 3/2 + 2i/3\).
2.9. \(\quad z_9 = 22 - 33i\).
2.10. \(\quad z_{10} = 333 + 22i\).
2.11. \(\quad z_{11} = 2i - 2\).
2.12. \(\quad z_{12} = -3i - 2\).
Q3
Find the complex conjugate for every complex number in Q2.
Q4
Draw \(z_1, z_4, z_5, z_7\) and their conjugates on the same Argand diagram, making sure to label both your axes and each complex number on the diagram. Can you spot a relationship between a complex number and its conjugate, with respect to the Argand diagram?
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 10/24 by tdhc.