Scroll back to the top

Virtual Math Learning Center Logo

Section 2.4 – Complex Numbers

Section Details.
  • Definition of complex numbers and the real and imaginary parts
  • The conjugate of a complex number
  • Operations with Complex Numbers


Practice Problems


Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
Consider the complex numbers \(z_1=4+\sqrt{-18}\) and \(z_2=2+\sqrt{-50}\).
 
  1. ​Write \(z_1\) and \(z_2\) in standard form.

    \(z_1=4+3\sqrt{2}i\)
    \(z_2=2+5\sqrt{2}i\)


    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V1

  2. Find \(z_1+z_2\), \(z_1-z_2\), and \(z_1z_2\)

    \(z_1+z_2=6+8\sqrt{2}i\),
    \(z_1-z_2=2-2\sqrt{2}i\)
    \(z_1\cdot z_2=-22+26\sqrt{2}i\)

    Video Errata: On \(z_1+z_2\), \(3\sqrt{2}+5\sqrt{2}=8\sqrt{2}\) not 7.
     

    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V2

  3. Find the conjugate of \(z_2\) 

    The conjugate of \(z_2\) is \(2-5\sqrt{2}i\)



    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V3