Section 2.4 – Complex Numbers
- Definition of complex numbers and the real and imaginary parts
- The conjugate of a complex number
- Operations with Complex Numbers
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Consider the complex numbers \(z_1=4+\sqrt{-18}\) and \(z_2=2+\sqrt{-50}\). Write \(z_1\) and \(z_2\) in standard form.
\(z_1=4+3\sqrt{2}i\)
\(z_2=2+5\sqrt{2}i\)
\(z_2=2+5\sqrt{2}i\)
2. Consider the complex numbers \(z_1=4+\sqrt{-18}\) and \(z_2=2+\sqrt{-50}\). Find \(z_1+z_2\), \(z_1-z_2\), and \(z_1z_2\)
\(z_1+z_2=6+8\sqrt{2}i\)
\(z_1-z_2=2-2\sqrt{2}i\)
\(z_1\cdot z_2=-22+26\sqrt{2}i\)
\(z_1-z_2=2-2\sqrt{2}i\)
\(z_1\cdot z_2=-22+26\sqrt{2}i\)
3. Consider the complex numbers \(z_1=4+\sqrt{-18}\) and \(z_2=2+\sqrt{-50}\). Find the conjugate of \(z_2\)
The conjugate of \(z_2\) is \(2-5\sqrt{2}i\)