1. Chapter 5 Section 4: Complex Numbers

2. VOCABULARY Not all quadratics have real- number solutions. For instance, x 2 = -1 has no real-number solutions because the square of any real number x is never negative.

3. THE SQUARE ROOT OF A NEGATIVE NUMBER PROPERTY NAME PATTERN EXAMPLE If r is a positive real number then By Property (1), it follows that

4. SOLVING A QUADRATIC EQUATIONS 1. s 2 = -13 2. 2x 2 + 11 = -37

5. COMPLEX NUMBERS (a + bi) REAL IMAGINARY PURE IMAGINARY (a + 0i) (a + bi)( b  0) (0 + bi)( b  0) -1 2 + 3i - 4i  5 – 5i 6i A complex number written in standard form is a number a + bi where a and b are real numbers. The number a is the real part of the complex number, and the number bi is the imaginary part.

6. ADDING AND SUBTRACTING COMPLEX NUMBERS (4 – i) + (3 + 2i) (7 – 5i) – (1 – 5i)

7. MULTIPLYING COMPLEX NUMBERS (4 – i)(3 + 2i) (7 – 5i)(1 – 5i)