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Multiplying Complex NumbersAdapted from Walch Education

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 Numbers2

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, a2 (bi)2, which can be simplified. a2 b 2i 2 = a2 b2 (1) = a2 + b2

4.3.3: Multiplying Complex Numbers3

PracticeFind the result of i 2 5i.4.3.3: Multiplying Complex Numbers4The SolutionSimplify 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 Numbers5

Can youFind the result of (7 + 2i)(4 + 3i). 4.3.3: Multiplying Complex Numbers6Thanks for watching~ms. dambreville