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Chapter 5 Section 4: Complex Numbers

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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.

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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

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

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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.

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

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

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Solve the quadratic equation x 2 + 1 = 0. Solving for x, gives x 2 = – 1 We make the following definition: Bell Work #1.

Solve the quadratic equation x 2 + 1 = 0. Solving for x, gives x 2 = – 1 We make the following definition: Bell Work #1.

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