📚 Topic Summary
Dividing complex numbers involves eliminating the imaginary part from the denominator. To do this, we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number $a + bi$ is $a - bi$. This process leverages the fact that $(a + bi)(a - bi) = a^2 + b^2$, resulting in a real number in the denominator.
This printable activity will guide you through understanding and applying this concept through vocabulary, fill-in-the-blanks, and a critical thinking question.
🧮 Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. Complex Number |
A. The result of multiplying a complex number by its conjugate. |
| 2. Conjugate |
B. A number of the form $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit. |
| 3. Imaginary Unit |
C. A method to rationalize the denominator when dividing complex numbers. |
| 4. Real Number |
D. A number that, when multiplied by a complex number, eliminates the imaginary part. |
| 5. Rationalization |
E. The square root of -1, denoted as $i$, where $i^2 = -1$. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
To divide complex numbers, we multiply both the numerator and the denominator by the ________ of the denominator. This process, known as ________, eliminates the ________ part from the denominator, leaving us with a ________ number. The conjugate of $a + bi$ is ________.
🤔 Part C: Critical Thinking
Explain why multiplying a complex number by its conjugate results in a real number. Use an example to illustrate your explanation.