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Published byCecil Blaise Stevens Modified over 6 years ago

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5.7.1 – Complex Numbers

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We used the method of square roots to solve specific types of quadratics Only used when we had problems such as x 2 – 16 = 0 In all cases, we were taking the square roots of positive numbers

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Negative Roots But, sometimes we may encounter problems such as; x 2 + 25 = 0 Yields the square root of a negative number Is this possible?

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Imaginary Number i To help us deal with this problem, we introduce the imaginary unit i Square Roots of Negative Number Properties 1) If r is a positive real number, then √-r = i √r Example; √-7 = i √7 2) i 2 = -1

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Example. Solve the equation 7x 2 = -49

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Example. Solve the equation 3x 2 + 5 = -4

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Example. Solve the equation 4x 2 + 4 = -12

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Try these 3 problems together. Make sure to note what kind of unit you will need. 1) 5x 2 – 10 = 15 2) -6x 2 = 600 3) 2x 2 + 10 = -10

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Assignment Pg. 264 3-8 all, 15-25 odd

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