Complex conjugates are pairs of complex numbers with the same real part, but opposite imaginary parts. For example, $a + bi$ and $a - bi$ are complex conjugates. When dividing complex numbers, we multiply both the numerator and the denominator by the conjugate of the denominator to eliminate the imaginary part from the denominator, resulting in a simplified expression.
This practice quiz will test your knowledge of complex conjugates and division. Get ready to solve some problems!
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Complex Conjugate | A. A number of the form $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit. |
| 2. Imaginary Unit | B. The process of eliminating the imaginary part from the denominator of a complex fraction. |
| 3. Complex Number | C. A number, denoted by $i$, such that $i^2 = -1$. |
| 4. Rationalizing the Denominator | D. The real part of a complex number $a + bi$. |
| 5. Real Part | E. A pair of complex numbers in the form $a + bi$ and $a - bi$. |
Complete the following paragraph using the correct terms:
To divide complex numbers, you multiply both the numerator and the denominator by the __________ of the __________. This process is called __________ the denominator. The goal is to eliminate the __________ part from the denominator.
Explain why multiplying a complex number by its complex conjugate always results in a real number. Provide an example to support your explanation.
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