1. Sec 3.3B: Complex Conjuget
Key Concepts
To divide two complex numbers of the form a + bi and c + di, where a, b, c and d are real numbers, rewrite the quotient as a fraction.
4.3.4: Dividing Complex Numbers

2. Concept: The Basic Look
In the following equation, let a, b, c, and d be real numbers.
4.3.4: Dividing Complex Numbers

3. Concept: The Basic Look cont. . .
Common Errors/Misconceptions
multiplying only the denominator by the complex conjugate
incorrectly determining the complex conjugate of the denominator
4.3.4: Dividing Complex Numbers

4. Concept: Guided Practice
Example 2
Find the result of (10 + 6i ) ÷ (2 – i ).
4.3.4: Dividing Complex Numbers

5. Concept: Guided Practice cont…
Rewrite the expression as a fraction.
Find the complex conjugate of the denominator.
The complex conjugate of a – bi is a + bi, so the complex conjugate of 2 – i is 2 + i.
4.3.4: Dividing Complex Numbers

6. Concept: Guided Practice cont…
Rationalize the fraction by multiplying both the numerator and denominator by the complex conjugate of the denominator.
4.3.4: Dividing Complex Numbers

7. ✔ Concept: Guided Practice cont…
If possible, simplify the fraction. The answer can be left as a fraction, or simplified by dividing both terms in the numerator by the quantity in the denominator. ✔
4.3.4: Dividing Complex Numbers