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5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.

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Imaginary Unit i i 2 = -1 i = √-1 The imaginary unit i can be used to write the square root of any negative number.

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The Square Root of a Negative Number

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Example 1: Solve a Quadratic Equation 7 x 2 = -49 3 x 2 – 5 = -29

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Checkpoint: x 2 = -3 x 2 = -20 x 2 - 4 = -12 x 2 = -7 x 2 + 3 = -2 2 x 2 + 7 = -17

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Complex Numbers Written in standard form is a number a + bi a and b are real numbers a is the real part of the complex number b is the imaginary part of the complex number

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Complex Numbers

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Examples 2 and 3: (3 + 2i) + (1 – i) (6 – 2i) – (1 – 2i) Add Complex NumbersSubtract Complex Numbers

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Checkpoint: (4 – 2i) + (1 + 3i) (3 – i) + (2 + 4i) (4 + 6i) – (2 + 3i) (-2 + 4i) – (2 + 7i) (1 – 2i) + (4 + 5i) (2 – i) – (-1 – 4i)

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p. 264 – 265 # 16 – 38 even, 59-63, 72, 73 Homework Day 1:

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Example 4: Multiply Complex Numbers 2i(-1 + 3i) (6 + 3i)(4 – 3i)

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Checkpoint: 3i(2 – i) (1 + 2i)(2 – i)

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Example 5: Dividing Complex Numbers 3 + 2i 1 – 2i 2 + i 1 - i

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p. 264 – 265 #40 – 58 even, 64-67, 74 Homework Day 2:

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