2. Multiplying Complex Numbers Adapted from Walch Education

3. Key Concepts Simplify any powers of i before evaluating products of complex numbers. Find the product of the first terms, outside terms, inside terms, and last terms. Note: The imaginary unit i follows the product of real numbers. 4.3.3: Multiplying Complex Numbers 2

4. Key Concepts, continued A complex conjugate is a complex number that when multiplied by another complex number produces a value that is wholly real. The complex conjugate of a + bi is a – bi, and the complex conjugate of a – bi is a + bi. The product of a complex number and its conjugate is the difference of squares, a 2 – (bi) 2, which can be simplified. a 2 – b 2 i 2 = a 2 – b 2 (–1) = a 2 + b 2 4.3.3: Multiplying Complex Numbers 3

5. Practice Find the result of i 2 5i. 4.3.3: Multiplying Complex Numbers 4

6. The Solution Simplify any powers of i. Multiply the two terms. Simplify the expression, if possible, by simplifying any remaining powers of i or combining like terms. 5(–i) = –5i 4.3.3: Multiplying Complex Numbers 5

7. Can you Find the result of (7 + 2i)(4 + 3i). 4.3.3: Multiplying Complex Numbers 6

8. THANKS FOR WATCHING ~ms. dambreville