5.1.5 Complex Numbers and Roots Key Objectives
• Define and use imaginary and complex numbers. • Solve quadratic equations with complex roots. Key Terms • An imaginary number i is the square root of a negative number. • The imaginary unit is defined as − 1. • A complex number is a number that can be written in the form a + bi where a and b are real numbers and = − i 1. • For a complex number of the form a + bi , a is the real part . • For a complex number of the form a + bi , the real number b is called the imaginary part . • The complex conjugate of any complex number a + bi is the complex number a − bi . Example 1 Simplifying Square Roots of Negative Numbers Square roots of negative numbers can be simplified and written in terms of i .
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