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Virtual Math Learning Center

Virtual Math Learning Center Texas A&M University Virtual Math Learning Center

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.

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

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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 \(z_1z_2\)

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

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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 \(2-5\sqrt{2}i\)

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