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Chapter 5 Section 4: Complex Numbers. VOCABULARY Not all quadratics have real- number solutions. For instance, x 2 = -1 has no real-number solutions because.

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Presentation on theme: "Chapter 5 Section 4: Complex Numbers. VOCABULARY Not all quadratics have real- number solutions. For instance, x 2 = -1 has no real-number solutions because."— Presentation transcript:

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 = x = -37

5 COMPLEX NUMBERS (a + bi) REAL IMAGINARY PURE IMAGINARY (a + 0i) (a + bi)( b  0) (0 + bi)( b  0) i - 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)


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